Device metrology targets and methods

ABSTRACT

Metrology methods and targets are provided, that expand metrological procedures beyond current technologies into multi-layered targets, quasi-periodic targets and device-like targets, without having to introduce offsets along the critical direction of the device design. Several models are disclosed for deriving metrology data such as overlays from multi-layered target and corresponding configurations of targets are provided to enable such measurements. Quasi-periodic targets which are based on device patterns are shown to improve the similarity between target and device designs, and the filling of the surroundings of targets and target elements with patterns which are based on device patterns improve process compatibility. Offsets are introduced only in non-critical direction and/or sensitivity is calibrated to enable, together with the solutions for multi-layer measurements and quasi-periodic target measurements, direct device optical metrology measurements.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a Continuation of International Patent ApplicationSerial No. PCT/US16/15782, filed Jan. 29, 2016, which claims the benefitof U.S. Provisional Patent Application No. 62/110,431 filed on Jan. 30,2015 and the benefit of U.S. Provisional Patent Application No.62/166,684 filed on May 27, 2015, which applications are incorporatedherein by reference in their entirety.

FIELD OF THE INVENTION

The present invention relates to the field of metrology, and moreparticularly, to target designs and methods of deriving measurementstherefrom.

BACKGROUND OF THE INVENTION

Metrology targets and methods aim at deriving measurements whichrepresent the production accuracy of designed devices. Metrology facesthe challenges of yielding measurable signals which reflect accuratelyproperties of the devices, at a rate that is high enough and a realestate that is low enough, to minimize the hindrances to the production.Current metrology overlay (OVL) algorithms uses special targets thathave periodic structures in two layers, which are offset differently indifferent target cells.

U.S. Patent Application Publication No. 2014/0316730, which isincorporated herein by reference in its entirety, discloses methods andsystems for performing semiconductor metrology directly on devicestructures using an on-the-fly model-based algorithm.

U.S. Patent Application Publication No. 2009/0244538, which isincorporated herein by reference in its entirety, discloses alithographic apparatus arranged to transfer a pattern from a patterningdevice onto a substrate with a reference set of gratings provided in thesubstrate, the reference set including two reference gratings havingline elements in a first direction and one reference grating having lineelements in a second, perpendicular, direction. US 2009/0244538 requiresidentical (or very similar) designs for x and y in order to calculatethe sensitivity of one direction and apply it to the second direction.However, this x-y design symmetry breaks in the device due to electricalfunctionality needs (and also the lithography process in critical layersis not symmetric).

U.S. Patent Application Publication No. 2011/0255066, which isincorporated herein by reference in its entirety, discloses measuringoverlays using multiple targets in multiple fields, assuming that theoverlay sensitivity of targets across the fields of the wafer isconstant, ignoring intra-field process variations.

Young-Nam Kim et al. 2009 (Device based in-chip critical dimension andoverlay metrology, Optics Express 17:23, 21336-21343), which isincorporated herein by reference in its entirety, discloses amodel-based in-chip optical metrology technique that allows directmeasurement of both critical dimensions and overlay displacement errorsin the DRAM manufacturing process, performed on the actual semiconductordevices without requiring special target structures.

SUMMARY OF THE INVENTION

The following is a simplified summary providing an initial understandingof the invention. The summary does not necessarily identify key elementsnor limits the scope of the invention, but merely serves as anintroduction to the following description.

One aspect of the present invention provides a method of directlymeasuring metrology parameters on devices, the method comprising: (i)measuring at least one metrology parameter from at least a portion of adevice design that is selected to have a plurality of irregularlyrepeating units, having specified features such as different sets oflines and cuts, along at least one direction of the portion, and (ii)calibrating sensitivity using at least one of: an intensity ofdiffraction orders orthogonal to the at least one direction, introducedoffsets along a non-critical direction, target cells with introducedoffsets adjacent to the device portion, and at least one sensitivitycalibration target, wherein the measuring is carried outscatterometrically on a plurality of targets to provide layer-specificmetrology parameters, at least one of the targets being part of thedevice portion having N>2 overlapping layers, wherein the plurality oftargets comprises at least one of: N cell pairs, each pair havingopposite offsets at a different layer; N cells with selected intendedoffsets; N or fewer cells with selected intended offsets configured toutilize pupil information; and N-cell calibration targets alongsidebetween N−1 and two overlay targets.

One aspect of the present invention provides a method comprising:configuring a multi-layered metrology target to have a plurality, M, oftarget cells over at least three, N≦M, target layers, each cell havingat least one periodic structure in each layer and configuring theperiodic structures of each cell to be offset with respect to each otherby specified offsets, measuring, scatterometrically, at least Mdifferential signals from the multi-layered metrology target, andcalculating scatterometry overlay (SCOL) metrology parameters from the Mmeasurements of the multi-layered metrology target by solving a set of Mequations that relate the SCOL metrology parameters to the differentialsignals and to the specified offsets.

One aspect of the present invention provides a method comprising:deriving a plurality of device-like patterns from a respective pluralityof device designs, wherein device-like patterns comprise specifiedfeatures such as one or more (different) sets of lines and cuts, anddesigning a metrology target using the derived device-like patterns asirregularly repeating units along at least one direction of the target.

One aspect of the present invention provides a method comprisingderiving at least one device-like pattern from a respective at least onedevice design, and designing a metrology target, comprising a pluralityof periodic structures, to have regions between the periodic structuresat least partially filled by the at least one device-like pattern.

One aspect of the present invention provides a method comprisingmeasuring, e.g., model free, at least one metrology parameter in atleast one target cell without introducing an intended offset along acritical measurement direction into the at least one target cell bycalibrating at least one sensitivity parameter using offsets in at leastone of: (i) an orthogonal, non-critical measurement direction and (ii)at least one additional target cell other than the at least one targetcell.

One aspect of the present invention provides a method of directlymeasuring metrology parameters on devices which combines theabove-mentioned methods synergistically.

These, additional, and/or other aspects and/or advantages of the presentinvention are set forth in the detailed description which follows;possibly inferable from the detailed description; and/or learnable bypractice of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of embodiments of the invention and to showhow the same may be carried into effect, reference will now be made,purely by way of example, to the accompanying drawings in which likenumerals designate corresponding elements or sections throughout.

In the accompanying drawings:

FIG. 1A is a high level schematic overview illustration of multilayertargets and measurement methods thereof, according to some embodimentsof the invention.

FIG. 1B is a high level schematic illustration of two types ofmultilayer targets and measurement methods thereof, according to someembodiments of the invention.

FIG. 2 is a high level schematic illustration of multilayer targets,according to some embodiments of the invention.

FIGS. 3A and 3B are high level schematic illustrations of multilayertargets, according to some embodiments of the invention.

FIG. 4 is a high level flowchart illustrating method, according to someembodiments of the invention.

FIGS. 5A-5D and 6A-6F are high level schematic illustrations ofquasiperiodic SCOL targets, according to some embodiments of theinvention.

FIGS. 7A and 7B present simulation results of the effect of the noiseintroduced by the non-periodic target design on the first orderamplitude, according to some embodiments of the invention.

FIGS. 8A-8E are high level schematic illustrations of SCOL targets withimproved correlation to device patterns, according to some embodimentsof the invention.

FIG. 9 is a high level flowchart illustrating method, according to someembodiments of the invention.

FIGS. 10 and 11 are high level schematic illustrations of devicealignments, according to some embodiments of the invention.

FIG. 12 is a high level schematic illustration of leading diffractionorders along the non-critical and critical measurement directions,according to some embodiments of the invention.

FIG. 13 is a high level schematic illustration of a target incorporatingan offset-less device portion, according to some embodiments of theinvention.

FIG. 14 presents a table with exemplary simulation results of theresulting sensitivity values for different combinations of the first andsecond cells designs, according to some embodiments of the invention.

FIG. 15 is a high level flowchart illustrating a method of measuringoverlays without introducing intended shift along the criticaldirections, according to some embodiments of the invention.

FIG. 16 is a high level schematic illustration of a composite devicetarget, according to some embodiments of the invention.

FIG. 17 is a high level flowchart illustrating an integrative method ofmeasuring device overlays directly on the device, according to someembodiments of the invention.

DETAILED DESCRIPTION OF THE INVENTION

Prior to the detailed description being set forth, it may be helpful toset forth definitions of certain terms that will be used hereinafter.

The terms “metrology target” or “target” as used herein in thisapplication, are defined as any structure designed or produced on awafer which is used for metrological purposes. Specifically, overlaytargets are designed to enable measurements of the overlay between twoor more layers in a film stack that is produced on a wafer. Exemplaryoverlay targets are scatterometry targets, which are measured byscatterometry at the pupil plane and/or at the field plane, and imagingtargets.

Exemplary scatterometry targets may comprise two or more either periodicor aperiodic structures (referred to in a non-limiting manner asgratings) which are located at different layers and may be designed andproduced one above the other (termed “grating-over-grating”) or oneadjacent to another from a perpendicular point of view, termed“side-by-side”). Target designs include one or more cells, the term“cell” as used herein in this application, is defined as a part of atarget that is used to derived a measurement signal. Commonscatterometry targets are referred to as SCOL (scatterometry overlay)targets, DBO (diffraction based overlay) targets and so forth. Commonimaging targets are referred to as Box-in-Box (BiB) targets, AIM(advance imaging metrology) targets, AIMid targets, Blossom targets andso forth. It is noted that in the present invention, SCOL is related toas being model-free in the sense that the details of measured stack mustnot be known prior to the measurements and that no modelling of thetarget is necessarily required in order to extract the parameters. It isfurther noted that the invention is not limited to any of these specifictypes, but may be carried out with respect to any target design.

Target elements comprise periodic structures, having elements repeatingat one or more pitches, such as gratings. Certain metrology targetsexhibit an “induced offset”, also termed “intended offset”, “designedoffset” or “designed misalignment”, which is, as used herein in thisapplication, an intentional shift or overlay between the periodicstructures of the target. The term “overlay” as used herein in thisapplication, is defined as the overall offset, i.e., the intended offsetplus an unintentional offset, between two layers of a target or adevice. The unintentional offset may thus be derived by subtracting theintended shift from the measured overlay. Overlay targets are typicallydesigned to have pairs of cells, the cells of each pair having equal andopposite intended offsets, denoted ±f₀.

The term “periodic” as used herein in this application with respect to atarget or a target structure, is defined as them having a recurringpattern. The term “strictly periodic” as used herein in this applicationrefers to a target or a target structure which have a recurring unitcell which is identical at all recurrences. The term “quasi-periodic” asused herein in this application refers to a target or a target structurewhich have a recurring pattern which does not have a recurring unit cellbut rather exhibits a basic pattern such as a grid that underlies therespective element as well as multiple aberrations, for example, changesin the length, width or details of the recurring pattern, and/or changesin grid parameters and features. These aberrations may be judiciouslyselected (as explained) and/or may be random and/or may reflect designconsiderations. The effect of the aberrations on the signal, i.e., thedifference between signals derived from quasi-periodic targets andequivalent strictly periodic target is referred to in this applicationas “noise”, which may have random and systematic components. The noisemay be considered as part of the inaccuracy defined below (with respectto the strictly periodic design) and/or may be treated independentlythereof.

The terms “device” or “device design” as used herein in thisapplication, are defined as any part of the wafer which provides anoperating electronic circuit, such as e.g., memory devices or logicdevices. The term “critical direction” as used herein in thisapplication, is defined as a direction in the device design which issensitive to small offsets between layers (e.g., in the order ofmagnitude of 1 nm), with the device possibly malfunctioning if suchoffsets occur. The term “non-critical direction” as used herein in thisapplication, is defined as a direction in the device design which cantolerate small offsets (e.g., in the order of magnitude of 1 nm),without the device malfunctioning if such offsets occur.

The term “measurement direction” as used herein in this application, isdefined as a direction along which the overlay is measured. Whenperiodic targets are used there must be periodicity in the measurementdirection. The pitch is in the order of hundreds up to a few thousandsof nanometers. In addition to this coarse pitch there may be a typicallymuch smaller segmentation pitch of the features and\or a coarse pitch inthe orthogonal direction.

With respect to metrology measurements, the term “differential signal”as used herein in this application, is defined as the intensitydifference between two signals, such as the +1 and −1 diffraction ordersignals, measured from a target. The term “sensitivity” as used hereinin this application, is defined as a ratio, or relation, between thedifferential signal and the overall offset, or overlay, between periodicstructures along a respective measurement direction. The term“inaccuracy” as used herein in this application, is defined as adifference between a result of a measurement and the true value of themeasured quantity (measurand). It is underlined that while the presentedmodels are mostly linear, for clarity reasons, linearity is non-limitingin the sense that the algorithms may be adapted to utilize non-linearmodel, which are therefore part of the present disclosure as well.

In the following description, various aspects of the present inventionare described. For purposes of explanation, specific configurations anddetails are set forth in order to provide a thorough understanding ofthe present invention. However, it will also be apparent to one skilledin the art that the present invention may be practiced without thespecific details presented herein. Furthermore, well known features mayhave been omitted or simplified in order not to obscure the presentinvention. With specific reference to the drawings, it is stressed thatthe particulars shown are by way of example and for purposes ofillustrative discussion of the present invention only, and are presentedin the cause of providing what is believed to be the most useful andreadily understood description of the principles and conceptual aspectsof the invention. In this regard, no attempt is made to show structuraldetails of the invention in more detail than is necessary for afundamental understanding of the invention, the description taken withthe drawings making apparent to those skilled in the art how the severalforms of the invention may be embodied in practice.

Before at least one embodiment of the invention is explained in detail,it is to be understood that the invention is not limited in itsapplication to the details of construction and the arrangement of thecomponents set forth in the following description or illustrated in thedrawings. The invention is applicable to other embodiments that may bepracticed or carried out in various ways. Also, it is to be understoodthat the phraseology and terminology employed herein is for the purposeof description and should not be regarded as limiting.

Unless specifically stated otherwise, as apparent from the followingdiscussions, it is appreciated that throughout the specificationdiscussions utilizing terms such as “processing”, “computing”,“calculating”, “determining”, “enhancing” or the like, refer to theaction and/or processes of a computer or computing system, or similarelectronic computing device, that manipulates and/or transforms datarepresented as physical, such as electronic, quantities within thecomputing system's registers and/or memories into other data similarlyrepresented as physical quantities within the computing system'smemories, registers or other such information storage, transmission ordisplay devices.

Embodiments of the present invention provide efficient and economicalmethods and targets for measuring metrology parameters, in particularoverlays and particularly using model-free far field optical metrology,using device designs directly. Specifically, the following disclosureovercomes the three major barriers that prohibit prior art direct devicemeasurements, namely the multi-layer character of device designs, thenon-periodic nature of device designs and the inherent constraint ofhaving to avoid introduction of intended offset into actual devicedesigns (in order not to damage their electrical properties andperformance).

Metrology methods and targets are provided, that expand metrologicalprocedures beyond current technologies into multi-layered targets,quasi-periodic targets and device-like targets, without having tointroduce offsets along the critical direction of the device design.Several models are disclosed for deriving metrology data such asoverlays from multi-layered target and corresponding configurations oftargets are provided to enable such measurements. Quasi-periodic targetswhich are based on device patterns are shown to improve the similaritybetween target and device designs, and the filling of the surroundingsof targets and target elements with patterns which are based on devicepatterns improve process compatibility. Offsets are introduced only innon-critical direction and/or sensitivity is calibrated to enable,together with the solutions for multi-layer measurements andquasi-periodic target measurements, direct device metrologymeasurements.

The methods and targets are exemplified for optical scatterometryoverlay (SCOL) measurements of device structures, which is a fastnon-destructive overlay (OVL) technique. Its main limitation is the needfor special targets due to its limited resolution. These metrologytargets may have bad correlation with the actual device structuresbecause of the big deviations between their designs and locations. It istherefore desired to measure directly the device in order to betterreflect its OVL and other possible parameters of interest. The sectionlabeled “multi-layer targets” provides methodologies which enable SCOLmeasurements of overlapping multiple parallel patterning. The sectionlabeled “quasiperiodic targets” discloses how to handle device designsthat lack a unit cell and are not strictly periodic as well as how tohandle the signal to noise ratio in SCOL. The section labeled “fillingtargets gaps with device patterns” discloses how to enhance targetprocess compatibility. Finally, the section labeled “avoiding offsets indevice targets” presents innovative methods for sensitivity calculationwithout damaging the electrical properties. The disclosed methods,algorithms and target designs are combined synergistically into acomplete solution for on-device optical OVL measurements.

Multi-Layer Targets

First, multi-layer targets are disclosed together with correspondingmeasurement and signal derivation algorithms which enable theirmeasurement with no or small throughput/real-estate penalty. The targetsare discussed in a non-limiting manner in a one dimensional context andfor scatterometry overlay (SCOL) targets. Such targets and methods areexpected to improve upon current technologies at least on the followingaspects: (i) The design and measurements of optical overlay (OVL) ofin-die targets (which better reflect the device overlay) may be enabled;(ii) More flexibility in design of target dummification is provided,e.g., by allowing the features to be parallel to the measurementdirection; and (iii) The real estate and\or throughput specificationsmay be improved.

The present invention overcomes the limitation of the standardscatterometry overlay algorithm, which requires that the overlay betweentwo gratings is the only source of symmetry breaking. When additionalgratings are present, their relative offsets may vary the signal in away that cannot be treated using the standard overlay algorithm. Thiscontaminates the original two-layer overlay signal and results in aninaccurate measurement.

FIG. 1A is a high level schematic overview illustration of multilayertargets and measurement methods thereof, according to some embodimentsof the invention. Prior art overlay targets and algorithms 90 relate totwo-layered targets and respective overlay algorithms, which use atleast two measurement cells having opposite predefined offsets ±f₀ alongeach measurement direction. It is emphasized that applying prior artalgorithms to targets with more than two layers results in an excessivenumber of variables due to the interaction between the illumination andthe target layers. For example, prior art algorithms provide twoequations (corresponding to the two target cells with opposite offsets)to derive two variables (the relative shifts between the layers, i.e.,the overlay, and the coefficient A that related the overlay to thedifferential signal). In case of N>2 target layers, the two equationsprovided by prior art overlay algorithms are not sufficient to derivethe overlays between the N layers.

The present disclosure proposes methods 100 and overlay targets 290 withthree or more layers that enable extraction of various metrologyparameters, represented herein by overlays, from multi-layered targets.

Certain embodiments propose using modified overlay algorithms, as amethod 100A, to measure targets 201 having a plurality, N, of 2-celltargets, one cell pair for each of the N layers, all cells beingidentical but for a corresponding pair of cells for each layer, whichhave intended offsets ±f₀ along the measurement direction. For example,each target may comprise two periodic layers configured to measureoverlays between respective layers. The overlays may be derived frommeasurements of targets 201 by modified versions of prior art algorithms90 which take into account the intermediate layers. However, thisinnovative solution suffers from the following drawbacks: (i) thetargets are very different from the device (increasing thedevice-to-metrology bias) and (ii) the targets are less printable, evenon the scribe-line, due to their being farther away from the desiredprocess window. While it is possible to measure all overlays by modifiedSCOL algorithm 100A using targets 201, the following methods (100B-D)prove to be significantly more efficient in conserving real-estate andreducing MAM-time.

Certain embodiments use a half of the number of cells, namely N cells(or more) for measuring N-layered targets by selecting the offsetsjudiciously (denotes as a matrix [f], and defined below) and measuringthe targets layer by layer, as explained and exemplified in Equations1-6, method 100B and targets 200 below.

Certain embodiments use even fewer cells, namely N−1 cells (or more) andpossibly even fewer cells than N−1, for measuring N-layered targets byselecting the offsets judiciously and utilizing pupil information(information in signals measured at the pupil plane with respect to thetarget of the metrology tool's optical system), as explained andexemplified in Equations 7-18, method 100C and targets 300 below. It isnoted that using fewer than N cells per target is advantageous withrespect to conservation of wafer real-estate and reduction of MAM(move-acquire-measure) time.

Certain embodiments use even fewer cells, namely as few as two cells (ormore) 300 set near devices for measuring N-layered targets by selectingthe offsets judiciously and utilizing pupil information, as well as byusing additional calibration targets 200 which may be positioned atregions farther away from the devices, e.g., on scribe lines, asexplained and exemplified in Equation 16C (based in the derivation inEquations 7-18), method 100D, targets 200, 300 and FIG. 1B below. It isnoted that method 100D uses and further develops methods 100B, 100C andtargets 200, 300.

Targets 290, 201, 200, 300 may be measured under different and possiblymultiple hardware and illumination configurations, e.g., using differentwavelengths to and/or illumination modes, using different polarizations,using different apodizers or varying other elements in the opticalsystem, to enhance calibrations and measurements, especially underapplications of methods 100C and 100D.

FIG. 1B is a high level schematic illustration of two types ofmultilayer targets 200, 300 and measurement methods 100 thereof,according to some embodiments of the invention. Two methods arepresented a first method 100B that uses an analysis of the differentialsignals from the multi-grating targets, and a second method 100C thatuses an approximated decomposition of the overlay reported by thestandard algorithm. Both methods rely on using the full pupilinformation in order to extract the additional needed information. Foreach method, non-limiting examples for three-layer targets are shown,with the calculations needed in order to infer the overlay values. It isnoted that the three-layer targets are used per measurement direction,i.e., with N=3 and two direction measurements X, Y, six cells are usedto measure the overlays among the three layers in both directions.Clearly, targets may be similarly designed to provide measurement alonga single (critical direction) only.

The following describes methods 100B, 100C as two non-exhaustive andnon-limiting examples of method 100 of measuring overlay parameters inmultiplayer SCOL metrology targets, i.e., targets which employ aplurality of periodic structures (related to in the following, in anon-limiting manner as gratings), that are designed to be printed onwafers 60. Possible combinations of methods 100B and 100C are suggestedafter the principles of each method are explained. FIG. 2 is a highlevel schematic illustration of multilayer targets 200, according tosome embodiments of the invention. FIGS. 3A and 3B are high levelschematic illustrations of multilayer targets 300, according to someembodiments of the invention.

FIG. 2 schematically illustrates target 200 comprising N cells 220 in Nlayers 210, each cell 220 having at least one periodic structure 230. Itis noted that the choice of an identical number (N) of cells and layersis made merely to simplify the explanation below, and does not limit thescope of the invention. The number of cells may be larger or smallerthan the number of layers as well (for the latter possibility seeadditional derivations below). Periodic structures 230 are overlapping(one above the other) characterized by predefined (intended) offsets(f_(1,n), relating to cell i and layer n) between cell layers 210, aswell as by uncontrolled (unintended) offsets (ε_(i,n), relating to celli and layer n) that are the aim of metrology method 100. Both offsetsare derived from signals 205 by estimation of the respective overlays,which are influence by both types of offsets. The measured signal infirst-order scatterometry overlay is the differential signal D 205,which is the intensity difference between the +1 and −1 diffractionorders when a target cell 220 is illuminated. Differential signal D 205is used as a non-limiting example, as the disclosed methods may be usedto measure differences between other diffraction orders as well asderived metrological measurements.

The signal from the i^(th) cell 220 of N-cell target can be approximatedas in Equations 1, and the terms B_(k) may be respectively defined, withf_(1,n) and δ_(i,n) being the predetermined and uncontrolled differentgrating offsets for layer n of the ith cell, respectively, and theparameters ε_(i,n)=f_(1,n)+δ_(i,n) are defined as the total offset.

$\begin{matrix}{{{D_{i}\left( {ɛ_{i,1},{ɛ_{i,2}\mspace{11mu} \ldots \mspace{14mu} ɛ_{i,N}}} \right)} = {\sum\limits_{n = 1}^{N}{\sum\limits_{m = 1}^{n - 1}\; {A_{n} \cdot A_{m} \cdot \left( {\delta_{i,m} - \delta_{i,n} + f_{i,m} - f_{i,n}} \right)}}}}\mspace{79mu} {D_{i} = {\sum\limits_{k = 1}^{N - 1}\; {B_{k} \cdot \left( {{OVL}_{k} + f_{i,N} - f_{i,k}} \right)}}}{B_{k} = {\sum\limits_{{n_{1}\mspace{11mu} \ldots \mspace{14mu} n_{N - 1}},{m_{1}\mspace{11mu} \ldots \mspace{14mu} m_{N - 1}}}\; {\left( {n_{k} - m_{k}} \right) \cdot a_{n_{1}\mspace{11mu} \ldots \mspace{14mu} n_{N - 1}} \cdot a_{m_{1}\mspace{11mu} \ldots \mspace{14mu} m_{N - 1}} \cdot {\sin \left( {\phi_{n_{1}\mspace{11mu} \ldots \mspace{14mu} n_{N - 1}} - \phi_{m_{1}\mspace{11mu} \ldots \mspace{14mu} m_{N - 1}}} \right)}}}}} & {{Equations}\mspace{14mu} 1}\end{matrix}$

The product A_(n)·A_(m) describes the optical signal coupling betweenlayers n and m, which is unknown but assumed to be independent of theoffsets. To find the relative offsets ε_(i,1) may be assumed, in anon-limiting manner, to be zero, and the coefficients A_(n) may benormalized (e.g., to define Ã_(n)=A_(n)/A₁) to reduce the number ofunknown parameters to with 2(N−1).

Standard overlay targets have two layers and therefore two unknownparameters, and the two cells are used to provide the required twomeasured signals. Method 100 comprises the development of a newformalism that is required to handle more than two overlapping gratings,in order to distinguish between the effects of the offsets of thedifferent layers on the signal. The inventors note that such challengehas not yet been handled due to the high level of complexity involved inthe design of the targets, in the theoretical analysis and in thepractical measurement procedures, all of which are disclosed in thepresent invention. In the next sections two innovative formalisms(corresponding to procedures 100B and 100C) are described anddemonstrated by simplified, non-limiting models. The inventors note thata person skilled in the art can easily expand these models to includeadditional contributions, e.g., higher diffraction orders, which arethus considered likewise a part of the present disclosure.

Method 100B uses the inspection of differential signals 205 from targets200 to obtain overlays 235 (notated—OVL). Two variants of method 100Bare presented—one assuming that the values of the previous OVLs areknown, and a more advance variant that uses the pupil information inorder to obtain all OVL values in the design, without a priori knowledgeof the OVLs.

Method 100B begins with designing target 200 with N cells 220, each withN layers 210 featuring predetermined offsets f_(1,k), denoting theoffsets at cell i and layer k and presented as matrix f in Equations 2.As explained above, the choice of the same number of cells and layers isnon-limiting. The N×(N−1) differential-offset matrix F, and the(N−1)×(N−1) differential differential-offset matrix G are defined inEquations 2, and the differential differential-signal vector Δ isdefined and related to matrix G in Equations 3, based on Equations 1.The inventors have found out, that selecting the offset values of f in away that yields an invertible (non-singular) matrix G enables thederivation of the overlay values from the target measurements, as shownexplicitly below. The specific values of f_(1,k) may be selectedjudiciously depending on device specifications, and are generally below1/30 of the target pitch.

$\begin{matrix}{\mspace{79mu} {{f = \begin{pmatrix}f_{1,1} & f_{1,2} & \ldots & f_{1,N} \\f_{2,1} & f_{2,2} & \ldots & f_{2,N} \\\vdots & \vdots & \ddots & \vdots \\f_{N,1} & f_{N,2} & \ldots & f_{N,N}\end{pmatrix}}{F = {\begin{pmatrix}F_{1,1} & F_{1,2} & \ldots & F_{1,{N - 1}} \\F_{2,1} & F_{2,2} & \ldots & F_{2,{N - 1}} \\\vdots & \vdots & \ddots & \vdots \\F_{N,1} & F_{N,2} & \ldots & F_{N,{N - 1}}\end{pmatrix} = \begin{pmatrix}{f_{1,1} - f_{1,N}} & {f_{12} - f_{1N}} & \ldots & {f_{1,{N - 1}} - f_{1N}} \\{f_{2,1} - f_{2,N}} & {f_{22} - f_{2N}} & \ldots & {f_{2,{N - 1}} - f_{2N}} \\\vdots & \vdots & \ddots & \vdots \\{f_{N,1} - f_{N,N}} & {f_{N\; 2} - f_{NN}} & \ldots & {f_{N,{N - 1}} - f_{NN}}\end{pmatrix}}}{G = {\begin{pmatrix}G_{1,1} & G_{1,2} & \ldots & G_{1,{N - 1}} \\G_{2,1} & G_{2,2} & \ldots & G_{2,{N - 1}} \\\vdots & \vdots & \ddots & \vdots \\G_{{N - 1},1} & G_{{N - 1},2} & \ldots & G_{{N - 1},{N - 1}}\end{pmatrix} = \begin{pmatrix}{F_{1,1} - F_{N,1}} & {F_{1,2} - F_{N,2}} & \ldots & {F_{1,{N - 1}} - F_{N,{N - 1}}} \\{F_{2,1} - F_{N,1}} & {F_{2,2} - F_{N,2}} & \ldots & {F_{2,{N - 1}} - F_{N,{N - 1}}} \\\vdots & \vdots & \ddots & \vdots \\{F_{{N - 1},1} - F_{N\; 1}} & {F_{{N - 1},2} - F_{N\; 2}} & \ldots & {F_{{N - 1},{N - 1}} - F_{N,{N - 1}}}\end{pmatrix}}}}} & {{Equations}\mspace{14mu} 2} \\{\mspace{79mu} {{{\Delta = \begin{pmatrix}\Delta_{1} \\\Delta_{2} \\\vdots \\\Delta_{N - 1}\end{pmatrix}},{B = \begin{pmatrix}B_{1} \\B_{2} \\\vdots \\B_{N - 1}\end{pmatrix}},\mspace{79mu} {\Delta_{i} = {{\sum_{k = 1}^{N - 1}\; {G_{ik}B_{k}}} = ({GB})_{i}}},{B = {G^{- 1}\Delta}}}\mspace{79mu} {{\Delta_{i} = {{D_{N} - D_{i}} = {\sum\limits_{k = 1}^{N - 1}\; {B_{k} \cdot \left\lbrack {\left( {f_{i,k} - f_{i,N}} \right) - \left( {f_{N,k} - f_{N,N}} \right)} \right\rbrack}}}},}}} & {{Equations}\mspace{14mu} 3}\end{matrix}$

As seen in Equation 3, the definitions of matrix G and vector Δ providetheir use in obtaining the coefficients B_(k) defined in Equations 1,which are in turn used to provide the overlay values from themeasurements (given the predetermined offset matrices and the measureddifferential signals). Accordingly, Equations 4 relate the overlayvalues OVL to the differentials signal D, the B vector and thepredefined offsets (in terms of elements on matrix F), for the N^(th)cell, and further provide the respective relations of the overlay valuesfor cells N−1 down to 2. This is the first variant of method 100Brelated to above.

$\begin{matrix}{{D_{N} = {{\sum\limits_{k = 1}^{N - 1}\; {B_{k} \cdot \left( {{OVL}_{k} - F_{N,k}} \right)}} = {{\sum\limits_{k = 1}^{N - 2}\; {B_{k} \cdot \left( {{OVL}_{k} - F_{N,k}} \right)}} + {B_{N - 1} \cdot \left( {{OVL}_{N - 1} - F_{N,{N - 1}}} \right)}}}}\mspace{79mu} {{OVL}_{N - 1} = {\frac{D_{N} - {\sum_{k = 1}^{N - 2}{B_{k} \cdot \left( {{OVL}_{k} - F_{N,k}} \right)}}}{B_{N - 1}} + F_{N,{N - 1}}}}} & {{Equations}\mspace{14mu} 4}\end{matrix}$

Thus, given (i) the measured differential signals, (ii) thepredetermined offset matrices, and (iii) the OVL values for all previouslayers (N−2 overlay values), the OVL of the current layer may becalculated. Equation 5 demonstrates this for the simple, non-limitingcase of target 200 having three layers.

$\begin{matrix}{{OVL}_{2} = {\frac{D_{3} - {B_{1} \cdot \left( {{OVL}_{1} - F_{3,1}} \right)}}{B_{2}} + F_{3,2}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

The non-limiting example of three layered target 200 is presentedexplicitly in Equations 6A-6C. The offset matrix f provides the F, G,and inverse G matrices (with G_(i,j) ⁻¹ being the i, j matrix element ofthe inverse of matrix G) as expressed in Equations 6A and the B vectoras expressed in Equations 6B.

$\begin{matrix}{\mspace{79mu} {{f = {\left. {f_{0}\begin{pmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{pmatrix}}\Rightarrow F \right. = {f_{0}\begin{pmatrix}1 & 0 \\0 & 1 \\{- 1} & {- 1}\end{pmatrix}}}},\mspace{79mu} {G = {f_{0}\begin{pmatrix}2 & 1 \\1 & 2\end{pmatrix}}},\mspace{79mu} {G^{- 1} = {\frac{1}{3f_{0}}\begin{pmatrix}2 & {- 1} \\{- 1} & 2\end{pmatrix}}}}} & {{Equations}\mspace{14mu} 6A} \\{B = {\begin{pmatrix}B_{1} \\B_{2}\end{pmatrix} = {{G^{- 1}\Delta} = {{\begin{pmatrix}G_{11}^{- 1} & G_{12}^{- 1} \\G_{21}^{- 1} & G_{22}^{- 1}\end{pmatrix}\begin{pmatrix}{D_{3} - D_{1}} \\{D_{3} - D_{2}}\end{pmatrix}} = {\begin{pmatrix}{{G_{11}^{- 1}\left( {D_{3} - D_{1}} \right)} + {G_{12}^{- 1}\left( {D_{3} - D_{2}} \right)}} \\{{G_{21}^{- 1}\left( {D_{3} - D_{1}} \right)} + {G_{22}^{- 1}\left( {D_{3} - D_{2}} \right)}}\end{pmatrix} = {\frac{1}{3\; f_{0}}\begin{pmatrix}{{{- 2}D_{1}} + D_{2} + D_{3}} \\{D_{1} - {2D_{2}} + D_{3}}\end{pmatrix}}}}}}} & {{Equations}\mspace{14mu} 6B}\end{matrix}$

Assuming a known value for OVL₁, Equation 6C provides OVL₂, which ishence readily calculable from measured differential signals from thethree cells of target 200.

$\begin{matrix}{{OVL}_{2} = {{\frac{D_{3} - {B_{1} \cdot \left( {{OVL}_{1} - F_{3,1}} \right)}}{B_{2}} + F_{3,2}} = {{\frac{D_{3} - {B_{1} \cdot \left( {{OVL}_{1} + f_{0}} \right)}}{B_{2}} - f_{0}} = {\frac{{3f_{0}D_{3}} - {\left( {{{- 2}D_{1}} + D_{2} + D_{3}} \right) \cdot \left( {{OVL}_{1} + f_{0}} \right)}}{\left( {D_{1} - {2D_{2}} + D_{3}} \right)} - f_{0}}}}} & {{Equations}\mspace{14mu} 6C}\end{matrix}$

The second, more advanced variant of method 100, related to herein asmethod 100C, overcomes the need for all previous OVL values by combiningthe information from all the pixels within the pupil and using the factthat the previous OVL values do not depend on the pixel position. Thelatter observation is used to define a cost function Ω which has a zerodifferential with respect to any OVL value (the example is with respectto OVL₁, in a non-limiting manner) as expressed and developed byEquations 7. The summation parameter q denotes the individual pixels inthe pupil plane signal. In certain embodiments, q may be summed over apart of the pupil, e.g., according to simulation-based optimizations.

$\begin{matrix}{\mspace{79mu} {{\Omega = {\sum\limits_{m = 1}^{N}{\sum\limits_{q \in {pupil}}\; \left\lbrack {{D_{m}(q)} - {\sum\limits_{k = 1}^{N - 1}\; {{B_{k}(q)} \cdot \left( {{OVL}_{k} - F_{mk}} \right)}}} \right\rbrack^{2}}}}{\frac{\partial\Omega}{\partial{OVL}_{l}} = {{\sum\limits_{m = 1}^{N}{\sum\limits_{q \in {pupil}}{{B_{l}(q)}\;\left\lbrack {{D_{m}(q)} - {\sum\limits_{k = 1}^{N - 1}\; {{B_{k}(q)} \cdot \left( {{OVL}_{k} - F_{mk}} \right)}}} \right\rbrack}}} = 0}}{{\sum\limits_{k = 1}^{N - 1}{\left\lbrack {\sum\limits_{m = 1}^{N}{\sum\limits_{q \in {pupil}}{{B_{l}(q)}{B_{k}(q)}}}} \right\rbrack \cdot {OVL}_{k}}} = {\sum\limits_{m = 1}^{N}{\sum\limits_{q \in {pupil}}{{B_{l}(q)}\;\left\lbrack {{D_{m}(q)} + {\sum\limits_{k = 1}^{N - 1}\; {{B_{k}(q)} \cdot F_{mk}}}} \right\rbrack}}}}{{\sum\limits_{k = 1}^{N - 1}{\sum\limits_{q \in {pupil}}{{B_{l}(q)}{{B_{k}(q)} \cdot {OVL}_{k}}}}} = {\frac{1}{N}{\sum\limits_{q \in {pupil}}{{B_{l}(q)}\; {\sum\limits_{m = 1}^{N}\; \left\lbrack {{D_{m}(q)} + {\sum\limits_{k = 1}^{N - 1}\; {B_{k}{(q) \cdot F_{mk}}}}} \right\rbrack}}}}}{{\sum\limits_{k = 1}^{N - 1}{\sum\limits_{q \in {pupil}}{{B_{l}(q)}{{B_{k}(q)} \cdot {OVL}_{k}}}}} = {\sum\limits_{q \in {pupil}}{{B_{l}(q)}\;\left\lbrack {{D_{N}(q)} + {\sum\limits_{k = 1}^{N - 1}\; {{B_{k}(q)} \cdot F_{Nk}}}} \right\rbrack}}}}} & {{Equations}\mspace{14mu} 7}\end{matrix}$

Equations 7 provide the relation between the overlays and the signalsmeasured at the pupil plane with respect to the metrology target, in themetrology tool. The overlays can be derived as OVL=W⁻¹ V using the(N−1)×(N−1) matrix W and an (N−1)×1 vector V defined by Equations 8, asEquations 7 imply W·OVL=V.

$\begin{matrix}{{{W_{lk} = {\sum\limits_{q \in {pupil}}{{B_{l}(q)}\; {B_{k}(q)}}}};}{V_{l} = {\sum\limits_{q \in {pupil}}{{B_{l}(q)}\;\left\lbrack {{D_{N}(q)} + {\sum\limits_{k = 1}^{N - 1}\; {{B_{k}(q)} \cdot F_{Nk}}}} \right\rbrack}}}} & {{Equations}\mspace{14mu} 8}\end{matrix}$

Continuing with the simple non-limiting example of three-layered target200 (see Equations 6A-6C) and using the advanced variant discussed above(Equations 7 and 8), the pupil information enables calculation of the Wand V according to Equations 9A, and the derivation of the overlayvalues from the matrices as OVL=W⁻¹ V according to Equation 9B.

$\begin{matrix}{\mspace{79mu} {{{W_{lk} = {\sum\limits_{q \in {pupil}}{{B_{l}(q)}\; {B_{k}(q)}}}};}\mspace{79mu} {V_{l} = {\sum\limits_{q \in {pupil}}{B_{l}\left( {D_{3} + {B_{1}F_{3,1}} + {B_{2}F_{3,2}}} \right)}}}\mspace{79mu} {{W = \begin{pmatrix}{\sum\limits_{q}\; {B_{1}B_{1}}} & {\sum\limits_{q}\; {B_{1}B_{2}}} \\{\sum\limits_{q}\; {B_{2}B_{1}}} & {\sum\limits_{q}\; {B_{2}B_{2}}}\end{pmatrix}},\mspace{79mu} {V = \begin{pmatrix}{\sum\limits_{q}{B_{1}\left( {D_{3} + {B_{1}F_{3,1}} + {B_{2}F_{3,2}}} \right)}} \\{\sum\limits_{q}{B_{2}\left( {D_{3} + {B_{1}F_{3,1}} + {B_{2}F_{3,2}}} \right)}}\end{pmatrix}}}}} & {{Equations}\mspace{14mu} 9A} \\{\mspace{79mu} {{OVL} = {{W^{- 1}{V\begin{pmatrix}{OVL}_{1} \\{OVL}_{2}\end{pmatrix}}} = {\begin{pmatrix}{\sum\limits_{q}\; {B_{1}B_{1}}} & {\sum\limits_{q}\; {B_{1}B_{2}}} \\{\sum\limits_{q}\; {B_{2}B_{1}}} & {\sum\limits_{q}\; {B_{2}B_{2}}}\end{pmatrix}^{- 1}\begin{pmatrix}{\sum\limits_{q}{B_{1}\left( {D_{3} + {B_{1}F_{3,1}} + {B_{2}F_{3,2}}} \right)}} \\{\sum\limits_{q}{B_{2}\left( {D_{3} + {B_{1}F_{3,1}} + {B_{2}F_{3,2}}} \right)}}\end{pmatrix}}}}} & {{Equation}\mspace{14mu} 9B}\end{matrix}$

FIGS. 3A and 3B are high level schematic illustrations of multilayertargets 300, according to some embodiments of the invention. FIGS. 3Aand 3B illustrate in a non-limiting manner three-layered target 300, thedisclosed principles may be implemented to multi-layered targets by aperson skilled in the art, hence the latter are considered likewise partof the disclosed invention.

Multilayer targets are not used in the prior art since the additionallayers (beyond two) are an additional symmetry breaking source whichcontaminates the overlay signal from the two layers and results ininaccurate measurement. In the following, the one or more additionallayer(s) are treated as inaccuracy source and their effect on the signalis characterized. The characterization is used (i) to eliminate theinaccuracy contribution of the additional layer(s) to the overlay of anoriginal two-layered target (which may be selected arbitrarily in target300); and (ii) to calculate the offset of the additional layer(s) withrespect to the original layers. These are part of method 100D (see FIG.1A), which may replace and/or augment methods 100B and 100C of measuringmultilayered targets 200, which was described above. Particularly, thedistinction between targets 200 and 300 is made merely to clarify theexplanations and not to limit the scope of the invention, as clearlymulti-layered targets may be design to combine the features of targets200 and 300.

FIG. 3A schematically illustrates a non-limiting case, in which top andintermediate layers 310, 320, respectively, are regarded as the originallayers for which an overlay is to be calculated, while bottom layer 330(which may be replaced by multiple layers) is regarded as the inaccuracysource. The effect of the bottom layer offset with respect to theintermediate layer is similar to a symmetry breaking due to side wallangle asymmetry. FIG. 3B schematically illustrates three layered target300 with designation of the refracted electric fields as defined below,upon illumination I. It is assumed for the sake of simplicity, in anon-limiting manner, that the periodic structures in layers 310, 320 330are parallel gratings with identical pitches. It is further assumed, ina non-limiting manner, that the leading orders of the refracted electricfield are E₁ ^(r)—the first order signal refracted off top grating 310,E₀₁₀—the field transmitted through top grating 210, refracted to thefirst order off middle grating 320, and transmitted through top grating310, and E₀₀₁₀₀—the field transmitted through top and middle gratings210, 220 respectively, refracted to the first order off bottom grating330, and transmitted through middle and top gratings 320, 310,respectively, as illustrated in FIG. 3B. The corresponding intensity ofeach of these fields as I₁ ^(r)=|E₁ ^(r)|², I₀₁₀=|E₀₁₀|², andI₀₀₁₀₀=|E₀₀₁₀₀|². Under the assumptions stated above, the overallintensity at a given collection pupil point is expressed by Equation 10,with

$\Delta_{n} = {\frac{2\pi}{P}ɛ_{n}}$

(ε_(n) as defined above) and θ₁ ^(r), θ₀₁₀ and θ₀₀₁₀₀ being therespective topographic phases; and the differential signal is expressedby Equation 11, with coefficients A_(ij) not depending on the layeroffsets.

$\begin{matrix}{{{E(k)}}^{2} = {I_{1}^{r} + I_{010} + I_{00100} + {E_{1}^{t}{E_{010}\left( {{^{- {\Delta}_{3}}^{{({\theta_{010} + \Delta_{2}})}}} + {^{{\Delta}_{3}}^{- {{({\theta_{010} + \Delta_{2}})}}}}} \right)}} + {E_{1}^{t}{E_{00100}\left( {{^{- {\Delta}_{3}}^{{({\theta_{00100} + \Delta_{1}})}}} + {^{{\Delta}_{3}}^{- {{({\theta_{00100} + \Delta_{1}})}}}}} \right)}} + {E_{00100} {E_{010}\left( {{^{- {{({\theta_{00100} + \Delta_{1}})}}}^{{({\theta_{010} + \Delta_{2}})}}} + {^{{({\theta_{00100} + \Delta_{1}})}}^{- {{({\theta_{010} + \Delta_{2}})}}}}} \right)}}}} & {{Equation}\mspace{14mu} 10} \\{{{{{D(k)} \equiv {{{E(k)}}^{2} - {{E\left( {- k} \right)}}^{2}}} = {{{A_{23}(k)}{\sin \left( {\Delta_{2} - \Delta_{3}} \right)}} + {{A_{13}(k)}{\sin \left( {\Delta_{3} - \Delta_{1}} \right)}} + {{A_{12}(k)}{\sin \left( {\Delta_{1} - \Delta_{2}} \right)}}}},\mspace{79mu} {{A_{23}(k)} \equiv {{- 4}E_{1}^{t}E_{010}{\sin \left( \theta_{010} \right)}}}}\mspace{79mu} {{A_{13}(k)} \equiv {{- 4}E_{1}^{t}E_{00100}{\sin \left( \theta_{010} \right)}}}\mspace{79mu} {{A_{12}(k)} \equiv {{- 4}E_{00100}E_{010}{\sin \left( \theta_{00100} \right)}}}} & {{Equation}\mspace{14mu} 11}\end{matrix}$

The differential signal of Equation 11 may be approximated as expressedin Equation 12, assuming

$\Delta_{1}^{2} = {\left( {\frac{2\pi}{P}ɛ_{1}} \right)^{2}1.}$D(k)≈A ₂₃(k)sin(Δ₂−Δ₃)+[A ₁₂(k)−A ₁₃(k)] sin(Δ₁)+A ₁₃(k)sin(Δ₃)−A₁₂(k)sin(Δ₂)   Equation 12

In a non-limiting manner, the offset of middle grating 320 may beselected as zero, and Equation 12 may be expressed as Equations 13, withthe definitions of f(k) and Ã₁(k).

$\begin{matrix}{{{D(k)} \approx {{{- {A_{23}(k)}}{\sin \left( {\frac{2\pi}{P}ɛ_{3}} \right)}} + {\left\lbrack {{A_{12}(k)} - {A_{13}(k)}} \right\rbrack {\sin \left( {\frac{2\pi}{P}ɛ_{1}} \right)}} + {{A_{13}(k)}{\sin \left( {\frac{2\pi}{P}ɛ_{3}} \right)}}}=={{\left\lbrack {{A_{13}(k)} - {A_{23}(k)}} \right\rbrack {\sin \left( {\frac{2\pi}{P}ɛ_{3}} \right)}} + {\left\lbrack {{A_{12}(k)} - {A_{13}(k)}} \right\rbrack {\sin \left( {\frac{2\pi}{P}ɛ_{1}} \right)}}}}{{{f(k)} \equiv {{A_{13}(k)} - {A_{12}(k)}}},{{{\overset{\sim}{A}}_{3}(k)} \equiv {{A_{13}(k)} - {A_{23}(k)}}}}{{D(k)} \approx {{{{\overset{\sim}{A}}_{3}(k)}{\sin \left( {\frac{2\pi}{P}ɛ_{3}} \right)}} - {{f(k)}{\sin \left( {\frac{2\pi}{P}ɛ_{1}} \right)}}}}} & {{Equations}\mspace{14mu} 13}\end{matrix}$

As a result of Equations 13, the overlay (OVL) between top and bottomlayers 310, 330, using a standard OVL algorithm (Equation 14, with ε_(.)^(±)=δ₃±f₀, and with D(±f₀) as the corresponding differential signals),is as expressed in Equation 15. The notation in Equations 14-18 uses δas the overlay OVL, while rOVL denotes the overlay reported by the SCOLalgorithm. rOVL and δ (the actual OVL) may differ due to inaccuracy).

$\begin{matrix}{{{rOVL}_{23}(k)} = {{f_{0}\frac{{D\left( f_{0} \right)} + {D\left( {- f_{0}} \right)}}{{D\left( f_{0} \right)} - {D\left( {- f_{0}} \right)}}} \approx {f_{0}\frac{{{{\overset{\sim}{A}}_{3}(k)}{\sin \left( {\frac{2\pi}{P}ɛ_{3}^{+}} \right)}} - {{f(k)}{\sin \left( {\frac{2\pi}{P}ɛ_{1}} \right)}} + {{{\overset{\sim}{A}}_{3}(k)}{\sin \left( {\frac{2\pi}{P}ɛ_{3}^{-}} \right)}} - {{f(k)}{\sin \left( {\frac{2\pi}{P}ɛ_{1}} \right)}}}{{{{\overset{\sim}{A}}_{3}(k)}{\sin \left( {\frac{2\pi}{P}ɛ_{3}^{+}} \right)}} - {{f(k)}{\sin \left( {\frac{2\pi}{P}ɛ_{1}} \right)}} - {{{\overset{\sim}{A}}_{3}(k)}{\sin \left( {\frac{2\pi}{P}ɛ_{3}^{-}} \right)}} + {{f(k)}{\sin \left( {\frac{2\pi}{P}ɛ_{1}} \right)}}}} \approx \approx {f_{0}\frac{{{{\overset{\sim}{A}}_{3}(k)}\frac{2\pi}{P}\left( {\delta_{3} + f_{0}} \right)} - {{f(k)}\frac{2\pi}{P}ɛ_{1}} + {{{\overset{\sim}{A}}_{3}(k)}\frac{2\pi}{P}\left( {\delta_{3} - f_{0}} \right)} - {{f(k)}\frac{2\pi}{P}ɛ_{1}}}{{{{\overset{\sim}{A}}_{3}(k)}\frac{2\pi}{P}\left( {\delta_{3} + f_{0}} \right)} - {{f(k)}{\sin \left( {\frac{2\pi}{P}ɛ_{1}} \right)}} - {{{\overset{\sim}{A}}_{3}(k)}\frac{2\pi}{P}\left( {\delta_{3} - f_{0}} \right)} + {{f(k)}\frac{2\pi}{P}ɛ_{1}}}} \approx {\delta_{3} - {\frac{f(k)}{{\overset{\sim}{A}}_{3}(k)}ɛ_{1}}}}} & {{Equation}\mspace{14mu} 14} \\{{{{rOVL}\left( {k,n} \right)} \approx {{\delta_{3}(n)} - {{\overset{\sim}{f}(k)}{ɛ_{1}(n)}}}}{{\overset{\sim}{f}(k)} = {\frac{{A_{13}(k)} - {A_{12}(k)}}{{A_{13}(k)} - {A_{23}(k)}} = \frac{1 - {\frac{E_{010}}{E_{1}^{t}}\frac{\sin \left( {\theta_{00100} - \theta_{010}} \right)}{\sin \left( \theta_{00100} \right)}}}{1 - {\frac{E_{010}}{E_{00100}}\frac{\sin \left( \theta_{010} \right)}{\sin \left( \theta_{00100} \right)}}}}}} & {{Equation}\mspace{14mu} 15}\end{matrix}$

Equation 15 shows that the measured rOVL per pixel can be separated intothe OVL between the top layers and a term that depends on the bottomlayer offset. In the latter term there is a separation of variables:Momentum dependency and bottom-layer offset. It is assumed that thefirst term does not depend on site while the second term does not dependon momentum.

A more general calculation can be used for improved accuracy (i.e.,—more diffraction modes, non-linear contributions). Mathematical methodsfor solving such systems are presented in WIPO Publication No.PCT/US14/52670, which is to incorporated herein by reference in itsentirety.

In another version, continuing from Equations 13 using Equations 13A,the overlay between layers 1 and 2 may be derived using the standardoverlay algorithm, as expressed in Equations 14A.

$\begin{matrix}{{{{f(k)} \equiv {- {\frac{2\pi}{P_{1}}\left\lbrack {{A_{13}(k)} + {A_{12}(k)}} \right\rbrack}}},{{{\overset{\sim}{A}}_{1}(k)} \equiv {- \left\lbrack {{A_{13}(k)} - {A_{23}(k)}} \right\rbrack}}}{{D(k)} \approx {{{{\overset{\sim}{A}}_{3}(k)}{\sin \left( {\frac{2\pi}{P}ɛ_{3}} \right)}} - {{f(k)}{\sin \left( {\frac{2\pi}{P}ɛ_{1}} \right)}}}}} & {{Equations}\mspace{14mu} 13A} \\{{{{rOVL}(k)} = {\frac{P}{2\pi}{\tan^{- 1}\left( {\frac{2\pi}{P}\left( {\delta_{3} - {{\overset{\sim}{f}(k)}{\sin \left( {\frac{2\pi}{P}ɛ_{1}} \right)}}} \right)} \right)}}}{{\overset{\sim}{f}(k)} \equiv \frac{{A_{13}(k)} + {A_{12}(k)}}{A_{23}(k)}}} & {{Equations}\mspace{14mu} 14A}\end{matrix}$

If the signal from the bottom layer is smaller than the signal from thetop layer, or is in the order of magnitude thereof, a respectiveadditional approximation may be used and the overlay may be expressed asin Equation 15A, with n as the site index.

$\begin{matrix}{{{{\overset{\sim}{f}(k)}} = {{\frac{{A_{13}(k)} + {A_{12}(k)}}{A_{23}(k)}}1}}{{{rOVL}\left( {k,n} \right)} \approx {{ɛ_{3}(n)} + {{\overset{\sim}{f}(k)}{ɛ_{1}(n)}}}}} & {{Equation}\mspace{14mu} 15A}\end{matrix}$

Equation 15A shows that the measured rOVL per pixel can be separatedinto the OVL between the top layers and a term that depends on thebottom layer offset. In the latter term the variables may be separatedinto a momentum dependency and a bottom layer offset. It is assumed thatthe first term does not depend on the site while the second term doesnot depend on momentum. Systems expressed in Equation 15A may be solvedusing WIPO Publication No. PCT/US14/52670, discussed above.

The following examples illustrate disclosed method 100D in simplenon-limiting cases of four cells with three layers and of a targetdesign with three cells.

In the non-limiting example of four cells (1 . . . 4) with three layers(1 . . . 3) it is assumed that the periodic structures in layer 2 havezero offsets in all cells; the periodic structures in layer 1: cells 1and 2 have offsets +f₁ while cells 3 and 4 have offsets −f₁ and allcells have an uncontrolled shift of δ₂; and the periodic structures inlayer 3: cells 1 and 3 have offsets +f₃ while cells 2 and 4 have offsets−f₃ and all cells have an uncontrolled shift of δ₃—as summarized inTable 1.

TABLE 1 Assumptions for the example. Cell Offset 1 Offset 2 Offset 3 1δ₂ + f₁ 0 δ₃ + f₃ 2 δ₂ + f₁ 0 δ₃ − f₃ 3 δ₂ − f₁ 0 δ₃ − f₃ 4 δ₂ − f₁ 0 δ₃− f₃

The standard OVL algorithm applied on differential signals from cells 1and 2, and from cells 3 and 4, gives the expressions of Equations 16A,followed by the derivation of {tilde over (f)}:

$\begin{matrix}{{{rOVL}_{12}(k)} \approx {\delta_{3} - {{\overset{\sim}{f}(k)}\left( {\delta_{2} + f_{1}} \right)}}} & {{Equations}\mspace{14mu} 16A} \\{{{rOVL}_{34}(k)} \approx {\delta_{3} - {{\overset{\sim}{f}(k)}\left( {\delta_{2} - f_{1}} \right)}}} & \; \\{{\overset{\sim}{f}(k)} = \frac{{{rOVL}_{12}(k)} - {{rOVL}_{34}(k)}}{{- 2}f_{1}}} & \;\end{matrix}$

Equation 17A presents the case that the vector OVL_(n) is projected on{tilde over (f)}, which is exactly the first layer shift (with anegative sign).

$\begin{matrix}{{\langle{\sum\limits_{k}\frac{{{rOVL}_{n}(k)} - {\langle{{rOVL}_{n}(k)}\rangle}}{{\overset{\sim}{f}(k)} - {\langle{\overset{\sim}{f}(k)}\rangle}}}\rangle} = {{- {\langle{\sum\limits_{k}\frac{{ɛ_{3}(n)} - {{\overset{\sim}{f}(k)}{ɛ_{1}(n)}} - {\langle{{ɛ_{3}(n)} - {{\overset{\sim}{f}(k)}{ɛ_{1}(n)}}}\rangle}}{{\overset{\sim}{f}(k)} - {\langle{\overset{\sim}{f}(k)}\rangle}}}\rangle}} = {{\langle{{\sum\limits_{k}\frac{{ɛ_{3}(n)} - {\langle{ɛ_{3}(n)}\rangle}}{{\overset{\sim}{f}(k)} - {\langle{\overset{\sim}{f}(k)}\rangle}}} - {\sum\limits_{k}\frac{{{\overset{\sim}{f}(k)}{ɛ_{1}(n)}} - {\langle{{\overset{\sim}{f}(k)}{ɛ_{1}(n)}}\rangle}}{{\overset{\sim}{f}(k)} - {\langle{\overset{\sim}{f}(k)}\rangle}}}}\rangle} = {- {ɛ_{1}(n)}}}}} & {{Equation}\mspace{14mu} 17A}\end{matrix}$

In the non-limiting example of three cells, e.g., looking at cells 1, 2and 3 of the previous example (Table 1), the standard OVL algorithmapplied on the differential signals from cells 1, 2 and from cells 1, 3(reversing the roles of the layers in the algorithm, which results in aninversion of {tilde over (f)}, see Equation 15 for details) gives theexpressions of Equations 16B, followed by the derivation of {tilde over(f)}:

$\begin{matrix}{{{rOVL}_{12}(k)} \approx {\delta_{3} - {{\overset{\sim}{f}(k)}\left( {\delta_{2} + f_{1}} \right)}}} & {{Equations}\mspace{14mu} 16B} \\{{{rOVL}_{13}(k)} \approx {\delta_{2} - {\frac{1}{\overset{\sim}{f}(k)}\left( {\delta_{3} + f_{3}} \right)}}} & \; \\{{\overset{\sim}{f}(k)} = {- \frac{{{rOVL}_{12}(k)} + f_{3}}{{{rOVL}_{13}(k)} + f_{1}}}} & \;\end{matrix}$

Equation 17B presents the projection of the vector OVL_(n) on {tildeover (f)}. As the offsets f₁ and f₃ are known (predetermined), both OVLscan be extracted.

$\begin{matrix}{{{\langle\left. \overset{\sim}{f} \middle| {rOVL}_{12} \right.\rangle} = {\delta_{2} + f_{1}}},{{\langle\left. \frac{1}{\overset{\sim}{f}} \middle| {rOVL}_{13} \right.\rangle} = {\delta_{3} + f_{3}}}} & {{Equations}\mspace{14mu} 17B}\end{matrix}$

Table 1 and Equations 16A, 16B, 17A, 17B may be extended to any numberof layers N>3.

{tilde over (f)}(k) may be obtain from actual measurements by any of thefollowing options. (i) {tilde over (f)}(k) may be extracted fromsimulations or by measurements at different conditions and assumingconsistency, as described in WIPO Publication No. PCT/US14/52670,discussed above. (ii) Subsampling may be measured across the wafers atdedicated (multi-layer) targets positioned next to standard targets andthe matching between the targets may be optimized as illustrated in theexamples above (Equations 16A-B and 17A-B). The calibration may beapplied to the full sampling or to the next wafers. Alternatively orcomplementarily, the differential signal analysis (methods 100B, 100C)may be applied to the calibration targets. (iii) Subsampling may bemeasured across the wafers at dedicated targets positioned next toexternal reference targets and the matching between the targets may beoptimized. The calibration may be applied to the full sampling or to thenext wafers. (iv) A principal-component analysis (PCA) may be performedon the subsamples to give the relative measure of {tilde over (f)}(k),and the absolute value can be calculated since the OVL is obtained fromthe multi-cell targets, as described above.

Returning to FIG. 1B, certain embodiments of method 100D may combine theuse of methods 100B and 100C. For example, two-cell targets 300 may beprinted on the wafer, together with a smaller number of (dedicated,calibration) multi-cell targets 200 (i.e., targets having three cells ormore). Multi-cell targets 200 may be sampled in order to obtain the{tilde over (f)}(k) function, either by the overlay decompositionmethod, or by inspecting the resulting differential signals andobtaining {tilde over (f)}(k) from to differential signal analysismethod 100B. Once {tilde over (f)}(k) is obtained, the OVL values may becalculated from the reported OVL of two-cell target(s) 300 usingEquation 16C, similar to Equations 16A and 16B.

δ₂ =

{tilde over (f)}(k)|rOVL(nmk)

_(k) −f ₁(n)

δ₃ =

rOVL(n,k)

_(k) −f ₁(n)−δ₂(n)−f ₃(n)   Equation 16C

It is noted that the assumption of three periodic structures (gratings)is a non-limiting one, presented here for simplification purposes only.In case of two (or more) measurement directions, respective periodicstructures may be added. In order to conserve wafer real-estate,calibration multi-cell targets 200 may be relative few whilemeasurements of two-cell targets 300 may be carried out using thecalibration derived therefrom.

More specifically, by studying the OVL distribution across the pupil ina linearity array of the bottom grating, {tilde over (f)}(k) may beextracted (for example—using principal component analysis). For allother sites on the wafer the “OVL” can be separated into OVL₂₃ (“commonto all pixels”) and OVL₁₂ (“per pixel inaccuracy”), as shown inEquations 18, generalizing on the examples above.

$\begin{matrix}\left\{ \begin{matrix}{{ɛ_{1}(n)} = {\langle\left. {\overset{\sim}{f}(k)} \middle| {{rOVL}\left( {n,k} \right)} \right.\rangle}_{k}} \\{{ɛ_{2}(n)} = 0} \\{{ɛ_{3}(n)} = {{\langle{{rOVL}\left( {n,k} \right)}\rangle}_{k} - {ɛ_{1}(n)}}}\end{matrix} \right. & {{Equation}\mspace{14mu} 18}\end{matrix}$

This enables dedicated multi-layered target measurements using two cells(of three layers).

Respective metrology measurements of any of targets 290, 201, 200, 300are also considered part of the present disclosure.

FIG. 4 is a high level flowchart illustrating method 100, according tosome embodiments of the invention. Method 100 may be carried out atleast partially by at least one computer processor. Computer programproducts and corresponding metrology modules are provided, whichcomprise a computer readable storage medium having computer readableprogram embodied therewith and configured to carry out method 100 atleast partially. Target design files as well as metrology measurementsof the targets are also provided.

Method 100 may comprise any of the following, separate or combined:modifying current OVL algorithms to operate on N cell pairs (2N cells),each pair with opposite offsets in one layer (method 100A) (e.g., eachtarget with two periodic layers configured to measure overlays betweenrespective layers); using only N cells, designed with specific intendedoffsets that enable derivation of the overlay of the measurements(method 100B); using pupil information to reduce the number of requiredcells to N−1 (method 100C), and using calibration targets to reduce thenumber of specific overlay targets below N−1, possibly down to 2 perN-layered target (method 100D).

Method 100 may comprise configuring a multi-layered metrology target tohave a plurality, M, of target cells over at least three, N≦M, targetlayers, each cell having at least one periodic structure in each layer(stage 110) and configuring the periodic structures of each cell to beoffset with respect to each other by specified offsets (stage 115).Method 100 may comprise measuring, scatterometrically, at least Mdifferential signals from the multi-layered metrology target (stage120), and calculating SCOL metrology parameters from the M measurementsof the multi-layered metrology target by solving a set of M equationsthat relate the SCOL metrology parameters to the differential signalsand to the specified offsets (stage 130). The SCOL metrology parametersmay be overlays between the N layers. Calculating 130 of the SCOLmetrology parameters may be carried out sequentially for consecutivelayers (stage 132), e.g., as in first variant 100B of method 100described above. For example, the SCOL metrology parameters may beoverlays between the N layers, and calculating 130 may be carried outaccording to Equations 2-4. Alternatively or complementarily,calculating 130 of the SCOL metrology parameters may be carried outsimultaneously for the layers (stage 135), e.g., as in second variant100C of method 100 described above, by carrying out the measuring at apupil plane with respect to the target (stage 137) and usingmeasurements of a plurality of pixel positions at the pupil plane (stage138). For example, the SCOL metrology parameters may be overlays betweenthe N layers, and calculating 130 may be carried out according toEquations 7-9B. In a non-limiting example, N=3, the SCOL metrologyparameters are overlays between the three layers, and calculating 130may be carried out according to Equation 15.

Certain embodiments comprise multi-layered metrology targets having aplurality of target cells over at least three target layers, each cellhaving at least one periodic structure in each layer, with the periodicstructures of each cell being offset with respect to each other byspecified offsets. The targets may provide SCOL measurements which arelikewise part of the present disclosure.

Method 100 provides multiple novel aspects, such as: The measurement ofSCOL targets with more than two overlapping parallel gratings withminimal inaccuracy penalty; Combination of two-cell and multiple-celltargets sampling for accurate measurements of multiple overlappinggrating targets; Targets and measurement methods which follow all in-diedevice layout restrictions including lateral and vertical constrainswith no inaccuracy penalty; Multi-cell multi-grating targets andmeasurement methods for improved throughput and\or real estate; Targetdesign optimization based on simulations taking into account all processand lithography steps and resultant patterns, rather than only the twospecific desired layers; Optimization of all layer patterns based on ananalytic model—the model predicts the optimal optical propertiesminimizing undesired contributions to the signal; Use of informationacross the pupil such as reflectivity, differential signals and\oroverlay in order to get the accurate overlay per layer; and thecombination of the aforementioned per-pixel response with multi-celloverlay calculation in order to obtain a calibration for the standardalgorithm such that the desired overlay can be obtained from a two-celltarget.

Quasiperiodic Targets

In the following, examples of quasiperiodic SCOL targets are presented,which are more similar to device patterns and are periodic at predefinedscales, but are not lattices. This means that the full structure cannotbe divided into smaller identical structures (unit cells). It is notedbelow, that actual device patterns may also, under certain circumstanceswhich are described below, considered quasiperiodic SCOL targets, and asshown below, do not have to include the intended shifts. Hence thefollowing disclosure enables measuring overlay of certain device designsdirectly, in spite of their non-periodicity.

FIGS. 5A-5D and 6A-6F are high level schematic illustrations ofquasiperiodic SCOL targets 400, according to some embodiments of theinvention. Targets 400 exemplify targets which fulfill the requirementsof various OVL/alignment techniques (e.g., SCOL, AIM, scanner alignmentmarks) for periodic target, yet are not periodic in the sense thattargets 400 and do not have a unit cell. While targets 400 have norepeating unit cell, the Fourier transform of targets 400 does revealperiodicity at some defined length scales corresponding to an effectivetarget pitch at an additional length scale, which may be much biggerthan the actual fine scale pitch. In the analysis of the measurements oftargets 400, the random parts which break the translation symmetry maybe treated as “noise” and may be averaged out using measurements oflarge areas or using multiple measurements of different target areas.Alternatively or additionally, measurement conditions may be chosen tominimize the contribution of translation-variant features, or theircontribution may be eliminated using sophisticated signal analysis,target design and\or hardware, as exemplified below. Respectivemetrology measurements of targets 400 are also considered part of thepresent disclosure.

In FIG. 5A, target 400 is illustrated schematically using a basicpattern of horizontal and vertical lines to indicate the quasi-periodicnature of target 400 (X and Y axes illustrate two measurement axes, theperiodicity along the Y axis may correspond to the pitch in standardSCOL targets). It is noted that in the details, elements 410-410F etc.of which target 400 is composed, each includes gaps and cuts whichmodify the elements and target 400 as a whole from being a regular grid,making target 400 grid-based but incorporating multiple irregularitiesthat are derived from device patterns as illustrated in FIGS. 5B and 5Cin an exemplary manner. FIGS. 6A-6F further elaborate on this aspect bydenoting target 400 as being made of blocks 410A-410F etc. (FIG. 6A)which are designed as schematic representations or abstractions ofdevice patterns (FIGS. 6B-6E) and may be combined to form quasi-periodictargets 400 (FIG. 6F). It is emphasized that all block designs are basedon a similar periodicity that is represented by the respective grids,yet include multiple irregularities or aberrations from the gridsymmetry, which overall yield quasi-periodic target 400.

FIG. 5B is a high level schematic illustration of a simplified devicelayout 420 (e.g., a NAND gate layout) as a basis for pattern 410Aexemplified in FIG. 5C. Pattern 410A comprise specified features, e.g.,features that may be derived from device layout 420 by furthersimplification, such as maintaining rows 411 from device layout 420 andusing various types of cuts 412 (analogous to metal lines connecting therows in the actual device layout) to yield pattern 410A as well asalternative patterns such as pattern 410E illustrated in FIG. 5D. FIG.5A schematically illustrates a combination of a plurality of patternsdenoted by 410A, 410B, 410C, 410D, 410E, 410F etc. which may likewise bevariations on the dimensions of pattern 410A and/or on the configurationof cuts 412 in it. Target 400 may thus be described as superposition ofrepeating unit cell and varying cuts, and/or may be designed to lack adefined repeating unit cell altogether. Different cuts in patterns410A-F may be selected to represent different logic gates. Theillustrated design may be provided for one or more layers of target 400.It is noted that the illustrated lines and cuts may be the result ofmultiple lithography steps (e.g., possibly creating the lines with pitchmultiplication processes) and then possibly multiple applications ofcuts. The patterns may however also be carried out in a singlelithography step. The illustrated lines and cuts serve to provide anon-limiting example for specified features of the patterns, and may bereplaced with other features with respect to device design.

FIG. 6A illustrates schematically targets 400 as quasi-periodic in thesense that they exhibit periodicity along the Y axis that results fromthe general organization of the wafer (Y direction periodicity, possiblyin the order of magnitude of the pitches of prior art targets) and aregularity along the X axis which results from the design principles ofthe wafer yet is not strictly periodic as designs 410A-410F etc. may notbe periodic, and designs 410A-410F etc. may be alternatednon-periodically. An evaluation of the degree of irregularity in thedesign of target 400 is presented below, and shown to still enablederivation of metrology signals and metrology parameters while takinginto account the deviations introduced by the irregularities.

An important and surprising insight the inventors gain from thedisclosed analysis is that devices and device sections may also beconsidered as quasi-periodic targets 400 and hence directly measuredusing metrology techniques and algorithms presented herein, underconsideration of the effects introduced by their “irregularities” asconsidered with respect to strict periodicity.

FIG. 6B schematically illustrates schemes 420B, 420C that representschematic layouts of NAND and NOT gates respectively (the backgroundgrid serves merely to illustrate the periodicity of the pattern and isnot an actual part of the pattern). In this exemplary process the M1pattern is produced using three lithography steps (denoted LELELE with Lstanding for a lithography step and E standing for an etch step, thethree steps applied to the same physical layer) to give thecorresponding M1a, M1b and M1c. FIG. 6C schematically illustrates onlythe M1 pattern which is common to 420B and 420C. Pattern 410C that maybe used to represent designs 420B, 420C in target 400. FIG. 6Dschematically illustrates schemes 420D, 420E that represent schematiclayouts of OR and AND gates respectively and FIG. 6E schematicallyillustrates corresponding M1 patterns 410B, 410D that may be used torepresent designs 420D, 420E in target 400. Clearly, additional patternsmay be used and integrated into target 400 according to variousperformance requirements and optimizations. It is noted that allillustrated designs 410A-410E illustrate the quasi-periodic nature oftargets 400 which maintain a large degree of periodicity whileintroducing irregularities in the patterns that correspond to specificdevice designs. FIG. 6F schematically illustrates a combination ofpatterns 420B, 420C, 420D that yields quasi-periodic target 400 (thebackground grid serves merely to illustrate the periodicity of thetarget and is not an actual part of the target). It is noted thatschemes 420A-E are used as a schematic adaptation of circuits such asthose presented by U.S. Pat. No. 8,863,063 and they serve asnon-limiting examples for possible schemes which may be used to derivecorresponding patterns 410A-F and other patterns.

FIGS. 7A and 7B present simulation results of the effect of the noiseintroduced by the non-periodic target design on the first orderamplitude, according to some embodiments of the invention. The noiserepresents irregularities in an essentially periodic structure, whichwas termed quasi-periodicity above. The following diagrams may be usedto estimate to what extent the deviations from periodicity, which wereexemplified in FIGS. 5A-5D and 6A-6F, degrade the metrology signalsderived from target 400. The pupil plane signal (amplitude) of a gratingwith irregularities was calculated using Fraunhofer approximation. InOVL measurement, modification dS in the first order noise roughlychanges the OVL by dS/A (A being the measurement sensitivity). Randomnoise was added to the grating in form of locations in which theamplitude was modified to zero. The random noise may be understood torepresent irregularities due to differences that arise from specificpatterns 410A-410F. The calculation was repeated for several differentillumination beam locations. The effect of the noise magnitude wascalculated for the first diffraction order amplitude distribution as afunction of beam location. In FIG. 7A the error bars indicate thestandard deviation of ten different beam locations. All values arenormalized with respect to the unperturbed intensity. FIG. 7B showsexplicitly the variability between the first order intensity whendifferent locations were sampled (corresponding to the error bars ofFIG. 7A). Different spatial distributions of the noisy points create anuncertainty of ca. 0.3% in the amplitude for a noise magnitude of 2%.FIGS. 7A and 7B illustrate that the deviation from strict periodicityresult in a controllable noise that represents the irregularities in thetarget design, and may be taken into account as an inaccuracy factorwhen deriving metrology results from targets 400. Moreover, FIGS. 7A and7B provide tools for handling noise due to irregularities in targetstructures, or in device designs which are used as targets, as suggestedbelow.

This inaccuracy may be treated either algorithmically (for example usingknown symmetry properties of the signal) or by selecting measurementpoints which cancel out the symmetry breaking. The latter can be donefor example by automatic analysis of the reticle.

Certain embodiments comprise metrology targets 400 having irregularlyrepeating units 410A-F along at least one direction of target 400(possibly two perpendicular directions), wherein the units comprisedevice-like patterns having one or more (different) sets of lines andcuts, which are derived from respective device designs. For example,unit lengths, characteristics of lines in the unit and/orcharacteristics of cuts in the unit may be varied along the at least onedirection of target 400. Target 400 may comprise two or more layers andmay provide SCOL measurements which are likewise part of the presentdisclosure.

Filling Targets Gaps with Device Patterns

Complementary to using quasi-periodic targets, the following presentsexamples of SCOL targets with improved correlation to device patterns.Such targets overcome prior art different reaction of different patternproperties in the presence of the same process conditions and theeffects of the patterns themselves on the process (forexample-micro-loading effect in dry etching). Clearly the presented SCOLtargets with improved correlation to device patterns may be usedindependently of the quasi-periodic targets disclosed above.

In standard OVL targets, the designers focus on the features to bemeasured and apply segmentation, OPC (optical proximity correction) andSRAF (sub-resolution assist features) to mimic the device behavior.However, a big portion of the target area, namely the area surroundingthe target features, the area between the features and the area inadditional layers which are not part of the OVL layers—is often nottaken into account during the design of the target. Sometimes parts ofthese areas are segmented or filled with dummy patterns, which often,however, have poor correlation to the device pattern and therefore maynot help or even damage the measurements.

The proposed targets improve the correlation of overlay measurement tothe actual device overlay error and reduce the differences betweenmeasurements on the target and the device properties. A source of thedifference in overlay between target and the device is related to thesurrounding in the vicinity of the target which is different than thesurrounding in the vicinity of the actual performing device structures.In order to improve the correlation, it is herein proposed that similardevice-like surrounding would surround each of the elements of thetarget. Concepts that enable such target design and surrounding arepresented below.

For example, all gaps within and around the targets and the targetelements may be filled with device patterns, which are selectedconsidering, e.g., (i) the pattern density (to provide sufficientmetrology sensitivity while maintaining the average density similar tothe device's pattern density), (ii) the similarity to the respectivedevice(s) (particularly when specific device patterns are identified asbeing critical for monitoring/control) and (iii) the pattern averageaspect ratio (as an important process parameter). Metrology and processsimulations may be used to select the proper device pattern. Since thedevice patterns may be unresolved using optical metrology, the selectedpatterns must not be strictly symmetrical, as standard metrology targetfeatures are selected to be. For example, device patterns may compriseactual or simplified device layouts, such as those demonstratedschematically in FIGS. 5B-5D and 6B-6F.

FIGS. 8A-8E are high level schematic illustrations of SCOL targets 500with improved correlation to device patterns, according to someembodiments of the invention. FIG. 8A schematically illustrates anextraction of a filling pattern 520, composed in the illustratednon-limiting example from patterns 520A, 520B at a previous layer and ata current layer, respectively. Pattern 520 may be derived from a devicepattern, e.g., similarly to the derivation described above (FIG. 5B), orin any other way that expresses device pattern features. Multipledifferent patterns 520 may be used in the following, in a regular or inan irregular manner. FIGS. 8B and 8C schematically illustrate sections510 of SCOL target 500 and of imaging target 500 (respectively) havingtarget elements 510 such as periodic structures, and pattern(s) 520filling regions between target elements 510. FIGS. 8D and 8Eschematically illustrate overviews of SCOL target 500 and of imagingtarget 500 (respectively) that illustrate the use of filling pattern 520around target elements 501 as well as in sub-regions of target 500within elements 501A, 501B of target 500, at the previous and/or at thecurrent layers. Filling pattern 520 may be used at any region orsub-region of targets 500, including sub-regions which are left free inFIGS. 8D and 8E (for clarity reasons). Embedded device-like structureswithin the target and between the cells of targets 500 may be selectedto mimic device surrounding and may be measured using eitherscatterometry or imaging techniques. Embedded device-like structures andpatterns may even, in certain cases, be introduced between elements ofperiodic structures of the targets, to the extent that the resultingdeterioration of the measured signal is kept within predefined bounds.

Certain embodiments comprise metrology targets 500 having a plurality ofperiodic structures 511 and regions between the periodic structureswhich are at least partially filled by at least one device-like pattern520 derived from a respective at least one device design. Sub-regionsbetween elements of the periodic structures may be at least partiallyfilled by at least one device-like pattern 520. Targets 500 may comprisetwo or more layers and may provide SCOL measurements which are likewisepart of the present disclosure.

Symmetry properties of the patterns that are used in the targets may beutilized in order to estimate and improve the signals receivedtherefrom. For example, patterns may be selected to enhance overlays dueto breaking of pattern symmetry by them, or signal symmetry propertiesmay be utilize to indicate specific inaccuracies.

FIG. 9 is a high level flowchart illustrating method 600, according tosome embodiments of the invention. Method 600 may be carried out atleast partially by at least one computer processor. Computer programproducts and corresponding metrology modules are provided, whichcomprise a computer readable storage medium having computer readableprogram embodied therewith and configured to carry out method 600 atleast partially. Target design files as well as metrology measurementsof the targets are also provided.

Method 600 may comprise deriving a plurality of device-like patternsfrom a respective plurality of device designs, wherein device-likepatterns comprise different sets of lines and cuts as exemplaryspecified pattern features (stage 615), and designing a metrology targetusing the derived device-like patterns as irregularly repeating unitsalong at least one direction of the target (stage 620).

Method 600 may comprise varying along the at least one direction of thetarget at least one of: a unit length, characteristics of lines in theunit and characteristics of cuts in the unit (stage 630). The at leastone direction may comprise two perpendicular directions of the target.The target may comprise at least two layers. Method 600 may compriseestimating a noise resulting from the target irregularities (stage 632),being the deviations from strict periodicity, and designing or selectingappropriate patterns according to specified noise thresholds (stage634). Method 600 may comprise estimating a measurement error accordingto the estimated noise (stage 636). Method 600 may comprise utilizingpattern symmetry properties to estimate and improve the signals receivedtherefrom (stage 638), as explained above (e.g., by treating theestimated noise algorithmically, using known symmetry properties of thesignal and/or by selecting measurement points which cancel out thesymmetry breaking, e.g., by automatic analysis of the reticle).

Method 600 may comprise producing the designed metrology target (stage650) and deriving a metrology signal from the produced metrology target(stage 660), with respect to the targets designed in stages 620 and/or630.

Method 600 may comprise deriving 610 at least one device-like patternfrom a respective at least one device design (stage 610), and designinga metrology target, comprising a plurality of periodic structures, tohave regions between the periodic structures at least partially filledby the at least one device-like pattern (stage 640). Method 600 maycomprise designing the metrology target to have sub-regions betweenelements of the periodic structures at least partially filled by the atleast one device-like pattern (stage 645). The targets may comprise twoor more layers. Method 600 may comprise producing the designed metrologytarget (stage 650) and deriving a metrology signal from the producedmetrology target (stage 660), with respect to the targets designed instages 640 and/or 645.

Avoiding Offsets in Device Targets

Returning to the basic SCOL assumption, it is assumed that the measureddifferential signal (intensity difference between the first andrespective minus first order) can be written as in Equation 19, with nbeing an index for the target cell (or target site) and E being thelateral offset between the two target periodic structures (e.g.,gratings) in the measurement direction.

D(n)=A(n)ε(n)   Equation 19

Since both the sensitivity A and the relative offset (or OVL) may changebetween targets, both parameters should be calculated per target, andthus two measurements with the same sensitivity and OVL are required. Ifthe sensitivity does not change, the OVL can be calculated usingEquation 20, but in reality this does not hold and using Equation 20 forOVL calculation results in big inaccuracy values.

$\begin{matrix}{{{OVL}(n)} = \frac{D(n)}{A}} & {{Equation}\mspace{14mu} 20}\end{matrix}$

In order to create two informative measurements, predetermined offsetsare applied by design. These offsets may damage the electricalproperties of the device and therefore cannot be applied on realdevices. Since for many OVL alignments there is only one criticaldirection, as illustrated schematically in FIGS. 10 and 11 below,offsets in the orthogonal direction may be applied without damaging thedevice and without affecting the final (after etch) pattern. Inconventional SCOL algorithms, offsets in the orthogonal direction do nothelp recover the sensitivity because the device pattern is not symmetricfor rotation of 90° and, as a consequence, the measurement of thesensitivity in this direction does not necessarily correlate with thedesired sensitivity. In the following derivations, linear approximationfor the differential signal is used for simplicity, in a non-limitingmanner. It is explicitly stated, that all methods disclosed below arevalid also using higher order approximations for the differential signaland such applications are considered part of the present disclosure. Thefollowing methods use orthogonal offsets information to derive metrologyparameters such as overlay, using orthogonal diffraction orders of thesame target which do not require any offsets and using orthogonaltarget(s) with a different design, having offsets in a non-criticaldirection, both options enabling potential use of actual devices astargets.

FIGS. 10 and 11 are high level schematic illustrations of devicealignments 97, according to some embodiments of the invention. Forexample, FIGS. 10 and 11 may represent an alignment of contacts 711 togates 712. FIGS. 10 and 11 schematically illustrate that the alignmentalong one direction (critical direction, denoted X) imposes muchstricter overlay requirements (smaller OVL values) than the alignmentalong the perpendicular direction (non-critical direction, denoted Y).FIG. 11 also illustrates schematically the first diffraction ordersignals 98 in the pupil plane (pupil image, for an exemplary centralillumination) of device 97, with +1 and −1 diffraction signals along theY direction (the direction perpendicular to the critical direction)being similar to each other (and having rotational symmetry) while the+1 and −1 diffraction signals along the X direction (the criticaldirection) differ from each other, e.g., in intensity due to overlaysymmetry breaking by elements 711.

In the following, the rotational symmetry along the non-criticalmeasurement axis is utilized to enable measurement along the criticalmeasurement axis without the present necessity to introduce designedoffsets along the critical measurement axis.

FIG. 12 is a high level schematic illustration of leading diffractionorders along the non-critical and critical measurement directions, 715,716 respectively, according to some embodiments of the invention. FIG.12 illustrates a simplified model for a grating over grating at the twodirections (represented as grating over grating model 725 and singlegrating model 726, as along the non-critical measurement directions thetop grating is non-periodic, see FIG. 11). It is noted that thesimplified model is presented for explanatory reasons, and does notlimit the invention. Gratings 701, 703 are to represent any periodicstructure, and equivalent models may be used for multi-layered periodicstructures. Moreover, the measured structures may be metrology targetsand/or actual devices. For example, model 725 may be seen asrepresenting effectively two-dimensional periodic structures whilemodels 726 may be seen as representing effectively one-dimensionalperiodic structures.

In model 725, the electric field on the collection pupil in the Xdirection is the interference between the two diffraction modesillustrated in FIG. 12 and represented in Equation 21. The notationsare: F and θ_(F) represent the amplitude and the phase factors,respectively, which are related to the gratings shapes of gratings 701,703; T and R represent the amplitudes that are related to theintermediate layers (702) while θ_(m) ₁ _(t) , θ_(m) ₁ _(r) are therespective phases. The grating pitch is P, while ε₁, ε₂ are thelocations of the gratings. Responsive of incident illumination 71, theelectric signal E is represented as the sum of component 75 reflectedoff upper grating 701 and component 76 reflected off lower grating 703,after passing through intermediate layer 702 and upper grating 701.

$\begin{matrix}{{E\left( {k = \frac{2\pi}{P}} \right)} \approx {{F\; ^{\theta_{m_{2}^{F}}}^{i\frac{2\pi}{P}ɛ_{2}}} + {F_{2}^{t}^{i\; \theta_{F_{2}^{t}}}T_{1}^{i\; \theta_{m_{1}^{t}}}F_{1}^{i\; \theta_{m_{1}^{F}}}^{i\frac{2\pi}{P}ɛ_{1}}R_{1}^{i\; \theta_{m_{1}^{r}}}F_{2}^{r}^{i\; \theta_{F_{2}^{r}}}}}} & {{Equation}\mspace{14mu} 21}\end{matrix}$

In model 725, the differential signal D_(ori) (intensity differencebetween respective plus and minus first diffraction orders) and theoverlay (OVL) sensitivity A (see Equations 19, 20) are expressed inEquations 22.

$\begin{matrix}{{D_{ori} = {4{FF}_{2}^{t}T_{1}F_{1}R_{1}F_{2}^{r}{\sin \left( {\theta_{F_{2}^{t}} + \theta_{m_{1}^{t}} + \theta_{m_{1}^{F}} + \theta_{m_{1}^{r}} + \theta_{F_{2}^{r}} - \theta_{m_{2}^{F}}} \right)}{\sin \left( {\frac{2\pi}{P}\left( {ɛ_{2} - ɛ_{1}} \right)} \right)}}}{A = {4{FF}_{2}^{t}T_{1}F_{1}R_{1}F_{2}^{r}{\sin \left( {\theta_{F_{2}^{t}} + \theta_{m_{1}^{t}} + \theta_{m_{1}^{F}} + \theta_{m_{1}^{r}} + \theta_{F_{2}^{r}} - \theta_{m_{2}^{F}}} \right)}}}} & {{Equations}\mspace{14mu} 22}\end{matrix}$

The sensitivity variation in a target (denoted n) with respect to somereference calibration target (denoted l), e.g., a reference targetprinted on the scribe lines and/or adjacent to actual design area, isexpressed in Equation 23:

$\begin{matrix}{\frac{A(n)}{A(1)} = \frac{4{F(n)}{F_{2}^{t}(n)}{T_{1}(n)}{F_{1}(n)}{R_{1}(n)}{F_{2}^{r}(n)}{\sin \left( {{\theta_{F_{2}^{t}}(n)} + {\theta_{m_{1}^{t}}(n)} + {\theta_{m_{1}^{F}}(n)} + {\theta_{m_{1}^{r}}(n)} + {\theta_{F_{2}^{r}}(n)} - {\theta_{m_{2}^{F}}(n)}} \right)}}{4{F(1)}{F_{2}^{t}(1)}{T_{1}(1)}{F_{1}(1)}{R_{1}(1)}{F_{2}^{r}(1)}{\sin \left( {{\theta_{F_{2}^{t}}(1)} + {\theta_{m_{1}^{t}}(1)} + {\theta_{m_{1}^{F}}(1)} + {\theta_{m_{1}^{r}}(1)} + {\theta_{F_{2}^{r}}(1)} - {\theta_{m_{2}^{F}}(1)}} \right)}}} & {{Equation}\mspace{14mu} 23}\end{matrix}$

When the OVL sensitivity is optimized, using proper selection of targetdesign and measurement conditions, the sine is maximized (having valueof 1 or −1), and hence its derivative is close to zero. It is thereforeassumed that small process variations (that may occur when differenttargets are compared) have a small effect on the sine term value. Inaddition it is assumed that the grating shape has negligible variations.Both assumptions are expressed in Equations 24.

$\begin{matrix}\left\{ \begin{matrix}{\frac{\partial{\sin \left( {\theta_{F_{2}^{t}} + \theta_{m_{1}^{t}} + \theta_{m_{1}^{F}} + \theta_{m_{1}^{r}} + \theta_{F_{2}^{r}} - \theta_{m_{2}^{F}}} \right)}}{\partial n} \approx 0} \\{\frac{\partial F}{\partial n} \approx 0} \\{\frac{\partial F_{2}^{t}}{\partial n} \approx 0} \\{\frac{\partial F_{1}}{\partial n} \approx 0} \\{\frac{\partial F_{2}^{r}}{\partial n} \approx 0}\end{matrix} \right. & {{Equations}\mspace{14mu} 24}\end{matrix}$

These assumptions enable the simplification of the sensitivityvariability Equation 23 into the approximated expression of Equation 25.

$\begin{matrix}{\frac{A(n)}{A(1)} \approx \frac{{T_{1}(n)}{R_{1}(n)}}{{T_{1}(1)}{R_{1}(1)}}} & {{Equation}\mspace{14mu} 25}\end{matrix}$

In model 726, the electric field E and the resulting measured intensityI_(p) are expressed in Equations 26 as component 77 reflected off lowergrating 703, after passing through intermediate layer 702 and upperlayer 701, the latter including the upper grating along the non-critical(non-measured) direction, and hence lacking periodicity. Notations areas in Equation 21.

$\begin{matrix}{{{E_{p}\left( \frac{2\pi}{P} \right)} \approx {F_{2}^{t}^{{\theta}_{F_{2}^{t}}}T_{1}^{{\theta}_{m_{1}^{t}}}F_{1}^{{\theta}_{m_{1}^{F}}}^{\frac{{2\pi}\;}{P}ɛ_{1}}R_{1}^{{\theta}_{m_{1}^{r}}}F_{2}^{r}^{{\theta}_{F_{2}^{r}}}}}\mspace{20mu} {{I_{p}\left( \frac{2\pi}{P} \right)} \approx {{F_{2v}^{t}T_{1}F_{1v}R_{1}F_{2v}^{r}}}^{2}}} & {{Equations}\mspace{14mu} 26}\end{matrix}$

Using a reference calibration target as described above (Equation 23),the relative intensity measured in model 726 may be expressed as inEquation 27.

$\begin{matrix}{\frac{I_{p}(n)}{I_{p}(1)} = \left( \frac{{F_{2v}^{t}(n)}{T_{1}(n)}{F_{1v}(n)}{R_{1}(n)}{F_{2v}^{r}(n)}}{{F_{2v}^{t}(1)}{T_{1}(1)}{F_{1v}(1)}{R_{1}(1)}{F_{2v}^{r}(1)}} \right)^{2}} & {{Equation}\mspace{14mu} 27}\end{matrix}$

Equations 28 present the assumption of minor variation in the gratingshape, and the resulting approximated expression for the relativemeasured intensity.

$\begin{matrix}\left\{ {{\begin{matrix}{\frac{\partial F_{2v}^{t}}{\partial n} \approx 0} \\{\frac{\partial F_{1v}}{\partial n} \approx 0} \\{\frac{\partial F_{2v}^{r}}{\partial n} \approx 0}\end{matrix}\frac{I_{p}(n)}{I_{p}(1)}} \approx \left( \frac{{T_{1}(n)}{R_{1}(n)}}{{T_{1}(1)}{R_{1}(1)}} \right)^{2}} \right. & {{Equations}\mspace{14mu} 28}\end{matrix}$

Combining the approximations expressed in Equations 25 and 28, and toadding in the angular information k across the pupil, Equation 29 usesEquations 28 to express the overlay sensitivity in the criticaldirection in terms of measurements along the non-critical direction andof measurements of the reference targets (p is constant).

$\begin{matrix}{\frac{A\left( {n,k} \right)}{A\left( {1,k} \right)} = {P\sqrt{\frac{I_{p}\left( {n,k} \right)}{I_{p}\left( {1,k} \right)}}}} & {{Equation}\mspace{14mu} 29}\end{matrix}$

The overlay (OVL) per pixel can thus be calculated based on a singlecell and the calibrated sensitivity, as expressed in Equation 30.

$\begin{matrix}{{{OVL}\left( {n,k} \right)} = \frac{D\left( {n,k} \right)}{{A\left( {1,k} \right)}P\sqrt{\frac{I_{p}\left( {n,k} \right)}{I_{p}\left( {1,k} \right)}}}} & {{Equation}\mspace{14mu} 30}\end{matrix}$

As stated above, more complex models and calibration functions may beimplemented using the same methodology and are considered part of thepresent disclosure. It is noted that the orthogonal diffraction ordermay also be used for calculation of geometrical properties of the target(for example: Critical Dimensions), with or without optical modeling.

The method expressed above in Equations 21-30 (see also method 800below) may be implemented in various ways to derive metrologymeasurements (of which the overlay was presented as non-limitingexample) from various device and target designs. As a non-limitingexample, FIG. 13 schematically illustrates one exemplary configurationfor the application of the method.

FIG. 13 is a high level schematic illustration of a target 700,incorporating an offset-less device portion, according to someembodiments of the invention. Target 700 may be designed to provide asensitivity calculation without introduction of offsets along criticalOVL dimension 715 (in cell 710), by using additional cell(s) 720 withpattern and offsets in different direction(s) 716 (e.g., perpendicularto the critical direction of cell 710). FIG. 13 illustrates in anon-limiting manner a three-cells designs in two layers, yet may beextended to a multi-layered design as explained above in the presentdisclosure, as well to quasi-periodic targets and devices as explainedabove. Target 700 enables overlay calculation along critical direction715 without the need to introduce intended offsets in this direction. Itis explicitly noted that cell 710 may be understood as representing atleast a portion of an actual device design, the disclosed method thusenabling measuring devices directly, without introducing offsets atleast along the critical direction of the device, possibly withoutintroducing any offsets into the device design.

Measurement of central cell 710 is used for the Y differential signalcalculation (in Equation 32 below), while other (e.g., two) cells 720have intended offsets ±f₀ and are designed to best fit the relation inEquation 31. These equations express the sensitivity A of one target asbeing approximated by a function of a second nearby target. In Equation31, n denotes the target\wafer position index, A_(v) denotes thesensitivity of the second target (the one used to approximatesensitivity A, represented in FIG. 13 as cells 720) and α₀, α₁, α₂ arecoefficients that may be derived using regression techniques, based oneither simulations or measurements.

A(n)=α₀+α₁ A _(v)(n)+α₂ A _(v)(n)²   Equation 31

Second target 720 may have gratings along different direction 716 fromfirst cell 710 (with periodic structures along critical direction 715).Moreover, the gratings geometry may be different and offsets ±f₀ may beintroduced between the gratings. Metrology simulations may be used tooptimize the behavior described in 0, possibly in combination withlithography and\or process simulations. The reported OVL in criticaldirection 715 becomes the one expressed in Equation 32.

$\begin{matrix}\begin{matrix}{{{OVL}(n)} = \frac{D(n)}{A(n)}} \\{= \frac{D(n)}{a_{0} + {a_{1}{A_{v}(n)}} + {a_{2}{A_{v}(n)}^{2}}}}\end{matrix} & {{Equation}\mspace{14mu} 32}\end{matrix}$

This method allows using different patterns in order to measure deviceswithout degrading its electrical properties (by introducing intendedoffsets). Note that this method allows using different measurementconditions (e.g., wavelength, polarization, etc.) for the calibrationmeasurement. The disclosed method may be implemented in different waysand be improved by various sources of information. For example,Equations 31 and 32 may be replaced by Equations 33 and 34 which usepupil information, treating each pixel k independently and calculatingthe overlay as an (possible weighted) average of the pupil pixels. Aweight function may be used, which takes into account different signalproperties per pixel, such as the quality of the relation expressed inEquations 29 and 33. Signal properties may be estimated in simulationsand/or be directly measured.

$\begin{matrix}{{A\left( {n,k} \right)} = {{a_{0}(k)} + {{a_{1}(k)}{A_{v}\left( {n,k} \right)}} + {{a_{2}(k)}{A_{v}\left( {n,k} \right)}^{2}}}} & {{Equation}\mspace{14mu} 33} \\\begin{matrix}{{{OVL}(n)} = {\langle\frac{D\left( {n,k} \right)}{A\left( {n,k} \right)}\rangle}_{k}} \\{= {\langle\frac{D\left( {n,k} \right)}{{a_{0}(k)} + {{a_{1}(k)}{A_{v}\left( {n,k} \right)}} + {{a_{2}(k)}{A_{v}\left( {n,k} \right)}^{2}}}\rangle}_{k}}\end{matrix} & {{Equation}\mspace{14mu} 34}\end{matrix}$

FIG. 14 presents a table with exemplary simulation results of theresulting sensitivity values for different combinations of first andsecond cells designs 710 and 720 respectively, according to someembodiments of the invention. The table presents the sensitivity asinaccuracy values (in nm, based on simulations), high sensitivitiesbeing above ca. 1 nm and low sensitivities below ca. 1 nm, anddemonstrates the effectivity of the disclosed method. Method 800 (seebelow and Equations 21-30 above) was tested on fifteen different targetdesigns and ninety process variations. For each cell, the OVL acrossprocess variations was calculated using Equation 34. The target designof the row was calibrated using the target of the column; the averageabsolute inaccuracy is reported in Table 1. The inaccuracy when Equation20 is used is specified in the right column for reference as anindication of the achieved improvement. For example: The number in row10, column 6 (or 300-200 vs. 100-400) is 0.6 nm. The number in row 10,rightmost column is 24.0 nm. This means that target 300-200 hasinaccuracy level of 24.0 when constant sensitivity is assumed (Equation20), but when its sensitivity is calibrated using target 100-400(Equation 34) the inaccuracy is reduced down to 0.6 nm. It can be seenthat the above methodology of Equation 34 is applicable and providesacceptable results. Pairs of target designs, which may be actually verydifferent from each other, can be selected to successfully improve thesensitivity to acceptable levels. This result is surprising in view ofthe differences between the targets.

Certain embodiments may use Equation 32 with directly mixing differentpupil locations (for example due to different pitches and wavelengths)while certain embodiments may use Equation 33 using a more sophisticatedcorrelation algorithm

Certain embodiments comprise targets having a design that is optimizedto improve the approximations (model assumptions) suggested by Equations24 and/or 28.

The number of cells in SCOL targets may be reduced using the methodsdescribed above. For example, relative offsets of N features in the samelayer may be measured using N+1 cells instead of 2N cells—the firstfeature sensitivity and OVL are calculated using two cells, and allother designs may have a single cell for which the calibrationsensitivity function may be used with respect to the first design.

Metrology procedures may also be improved, as after calculating thecalibration function (e.g., according to Equations 29 or 31) based onsimulations and\or measurements, the run sequence may compriseon-the-fly measurements of single cells and use of the orthogonaldirection signal to calibrate the sensitivity, using the calculatedcalibration function. It is noted that in case of unstable processes,several different calibration targets may be used.

FIG. 15 is a high level flowchart illustrating a method 800 of measuringoverlays without introducing intended shift along critical directions,according to some embodiments of the invention. Method 800 may beimplemented using the algorithm, expressed in Equations 21-30 above.Method 800 may be at least partially implemented by at least onecomputer processor, e.g., in a metrology module. Certain embodimentscomprise computer program products comprising a computer readablestorage medium having computer readable program embodied therewith andconfigured to carry out of the relevant stages of method 800. Certainembodiments comprise target design files of respective targets designedby embodiments of method 800.

Method 800 comprises measuring overlay(s) while avoiding prior artintroduction of intended offset(s) along a critical measurementdirection in at least one of the target cells (stage 805). The measuringmay be carried out in a model-free manner. Method 800 may comprisecalibrating sensitivity parameter(s) using offsets in an orthogonal,non-critical measurement direction (stage 810), using the intensity ofdiffraction orders orthogonal to the critical measurement direction.Alternatively or complementarily, method 800 may comprise designingreference calibration targets on scribe lines (stage 820) andcalibrating sensitivity parameter(s) using offsets in calibrationtarget(s) (stage 825). Method 800 may comprise selecting parameters ofreference targets to reduce inaccuracy according to the model (stage830). Method 800 may comprise using at least one additional target cellother than the at least one target cell to measure sensitivities (stage815), e.g., by introduced offsets (along either or both critical andnon-critical directions). The at least one additional target cell may beadjacent to the target cell(s) and/or be configured as separatecalibration targets.

Method 800 may comprise designing metrology targets that incorporate atleast a part of a device design, with cells having offsets at anon-critical direction while the device part exhibits no offsets (stage840). In certain embodiments, multiple parts of an actual device may beused and combined into a single metrology measurement, method 800further comprising selecting multiple device design portions to yield aderived pupil plane image from respective pupil images of the portions,which satisfies a specified criterion (e.g., with respect to periodicityand/or the estimated noise) (stage 845). For example, a pupil image usedin the OVL calculation may be an average of few pupil images measured atdifferent, possibly disparate device areas 50A. The selection of thecombination may be pre-defined or be carried out automatically in orderto effectively select the signal that provide certain characteristics,e.g., being most similar to a signal derived from a periodic target,exhibiting the lowest level of noise etc. Method 800 may compriseoptimizing target design according to the approximation assumptions(stage 850), e.g., by reducing variation in shape factors of theperiodic structures (stage 855). Offsets may be introduced along theorthogonal, non-critical measurement direction of the device designand/or in adjacent, non-device additional cells and/or in calibrationcells, e.g., on scribe lines.

The following aspects are provided by method 800 and the disclosureabove. OVL sensitivity calibration may be carried out based onon-the-fly information from additional diffraction orders, which mayinclude orthogonal diffraction orders. OVL sensitivity calibration maybe carried out based on on-the-fly information from a second target witha different design and/or from additional targets with different designsand\or diffraction orders reflectivity. These enable using OVL targetswith no offsets in the critical measurement direction (enabling directdevice measurements with no degradation in electrical functionality)according to the disclosed measurement methodology. Examples for targetwhich were presented above include any of: a one-cell SCOL target forone direction (x or y) in which the sensitivity is calculated based onorthogonal direction reflectivity; a three-cell SCOL target composed oftwo standard cells for the first direction and a third cell for theorthogonal direction; a SCOL target for N designs along a singledirection containing N+1 cells (instead of 2N) cells—a first design hastwo cells and all others have a single cell per design; and a SCOLtarget for N designs along a critical direction containing N+2 cells(instead of 21V) cells—two cells in the orthogonal non-criticaldirection and all others single cell without offsets per design. It isimportant to note that all the cells must not be adjacent to each other,for example the target may be a combination of cells located within thedevice active area and cells in its periphery.

The disclosure further provides OVL model-free measurements of targetswith at least one of: No intended offsets; no defined unit cell;multiple (more than two) overlapping patterning (i.e., differentlithography steps, possibly applied to the same physical layer); andmeasurement of device patterns using SCOL like algorithm (run timemodel-free approach). The methods enable optical measurements of devicepatterns after resist development as well as optical measurements offinal and after etch device patterns. The disclosure further providesmetrology-simulations-based target design optimization to match specificdevice patterns behavior as well as metrology simulations combined withlithography and\or process simulations for target design optimization tomatch specific device patterns behavior. Finally, model-free on-the-flyoptical OVL measurements using a single cell and combined OVL and OCD(optical critical dimension) targets with model-free OVL algorithm areprovided (possibly requiring measurements using multiple hardwareconfigurations, as explained above.

FIG. 16 is a high level schematic illustration of a composite devicetarget 700, according to some embodiments of the invention. FIG. 16illustrates in a schematic manner, the combination of the conceptsdisclosed above to yield direct metrology measurements in a device area50 (see below method 900). As illustrated in FIG. 16, a device regionmay be regarded as being multi-layered, quasi-periodic and as having nooffsets and/or offsets only in non-critical direction only. Thisunderstanding is surprising, as metrology target designs are usuallyvery different from device designs. However, the inventors have foundout, that from this perspective and/or by selecting specific deviceregions according to these criteria, actual device regions may besuccessfully treated and measured as metrology targets or parts thereofand provide useable metrology results, directly relating to devicecharacteristics. By considering and/or selecting device regions as beingmulti-layered, quasi-periodic in the sense described above and as havingno offsets and/or offsets only in non-critical direction only —therespective device regions may be used as target or target parts byapplying methods 100, 600 and 800 respectively, as illustrated in FIG.16.

For example, target 700 may comprise at least one region 50A of device50 as part 710 of the measured target in which no offsets are introduced(at least along critical directions with respect to the device'sfunctionality) and adjacent cells 720 which have intended offsets thatmay be used to derive device overlays according to pre-calculatedsensitivity parameters and/or calibration function(s). FIG. 16schematically illustrates an option of selecting one region 50A astarget part 710 adjacent to cells 720, as well as an option of selectingmultiple regions 50A as target part, possibly but not necessarilyadjacent to cells 720. Regions 50A may be selected to yield a derivedpupil plane image from respective pupil images of regions 50A, e.g., anaverage or a weighted average thereof, which satisfies a specifiedcriterion such as a noise threshold, a periodicity threshold or anyalgorithmic threshold used to optimize the selection in view of thequality of the derived signals and related overlay derivations.

Alternatively or complementarily, target 700 may comprise at least oneregion 50B of device 50 as target 700 or as a part thereof, which hasintended offsets introduced along non-critical direction(s) of thedevice design at specific region 50B. Such intended offsets may beselected to provide useful metrology information (e.g., sensitivityparameter A) without damaging the device performance (see explanationand derivation above, corresponding to FIGS. 10-12). Target 700 mayfurther comprise adjacent cells 720 which have intended offsets that maybe used to derive device overlays according to pre-calculatedsensitivity parameters and/or calibration function(s).

Direct device measurements may further utilize calibration targets 750,set e.g., on scribe lines, which calibrate any of the effects ofmulti-layers, quasi-periodicity and sensitivity, as explained above.Moreover, methods 100, 600 and/or 800 may be implemented synergisticallyas a method 900 described below, to enable direct measurements ofmetrology parameters on devices which are multi-layered and non-periodicwithout introducing offsets along critical direction of the devicedesigns.

FIG. 17 is a high level flowchart illustrating an integrative method 900of measuring device overlays directly on the device, according to someembodiments of the invention. Method 900 may be at least partiallyimplemented by at least one computer processor, e.g., in a metrologymodule. Certain embodiments comprise computer program productscomprising a computer readable storage medium having computer readableprogram embodied therewith and configured to carry out of the relevantstages of method 900. Certain embodiments comprise target design filesof respective targets designed by embodiments of method 900.

Method 900 may comprise using reference calibration targets and/ordevice-adjacent cells with intended offsets to enable direct measurementof device parts without introducing offsets into the device design(stage 910), e.g., implementing method 800. Method 900 may comprisecalibrating sensitivity using at least one of: introducing offsets alongnon-critical direction, using adjacent target cells with introducedoffsets, and using sensitivity calibration targets on scribe lines(stage 915), as explained above.

Method 900 may comprise extending the cell designs to multi-layeredmeasurements (stage 920), e.g., implementing method 100 in any of itsvariations 100A-D. Method 900 may comprise configuring additionaltargets to provide layer-specific metrology parameters usingmulti-layered (N) target cells (having N>2 overlapping layers)comprising at least one of: N cell pairs, each pair with oppositeoffsets at a different layer; N cells with selected intended offsets;N−1 or fewer cells with selected intended offsets configured to utilizepupil information; and calibration targets alongside overlay targetswith down to 2 cells (stage 925), as explained above.

Method 900 may comprise measuring quasi-periodic design patternsdirectly while managing and bounding resulting inaccuracies (stage 930),e.g., implementing method 600. Method 900 may comprise measuringmetrology parameters from at least a portion of a device design that isselected to have a plurality of irregularly repeating units, havingdifferent sets of lines and cuts as exemplary specified features, alongat least one direction of the portion (stage 935), as explained above.

Method 900 may comprise integrating the derivations for offset-less,multi-layer and quasi-periodic measurement algorithms (stage 940) todirectly measuring metrology parameters on devices (stage 950).

Method 900 may further comprise selecting parameters of the adjacenttarget cells and/or the sensitivity calibration targets to reduceinaccuracy according to a model of the inaccuracy (stage 955), asillustrated above.

Corresponding metrology targets comprise at least a portion of a devicedesign 710 that is selected to have a plurality of irregularly repeatingunits (e.g., as schematically exemplified in patterns 420A-E), havingdifferent sets of lines and cuts (e.g., as schematically exemplified intargets 400), along at least one direction of the portion, and aplurality of additional cells comprising multi-layer calibration cells(e.g., as schematically exemplified in targets 200 and 300) andsensitivity calibration cells (e.g., as schematically exemplified intargets 700 and 750). The multi-layer calibration cells may comprise anyof (see FIG. 1A): N cell pairs, each pair with opposite offsets at adifferent layer; N cells with selected intended offsets; N cells withselected intended offsets (or possibly fewer cells depending on themeasurement conditions and on algorithms used) configured to utilizepupil information; and N-cell calibration targets alongside overlaytargets with N−1 cells and optionally down to 2 cells, depending oncalibration conditions and algorithmic complexity. The sensitivitycalibration cells may comprise at least two additional cells havingintended offsets along the critical measurement direction of the atleast one target cell, e.g., additional cells having an orthogonalcritical measurement direction with respect to the at least one targetcell. The at least two additional cells may be adjacent to the deviceportion as additional cells 720 are. Respective metrology measurementsof the disclosed targets are also considered part of the presentdisclosure.

Aspects of the present invention are described above with reference toflowchart illustrations and/or portion diagrams of methods, apparatus(systems) and computer program products according to embodiments of theinvention. It will be understood that each portion of the flowchartillustrations and/or portion diagrams, and combinations of portions inthe flowchart illustrations and/or portion diagrams, can be implementedby computer program instructions. These computer program instructionsmay be provided to a processor of a general purpose computer, specialpurpose computer, or other programmable data processing apparatus toproduce a machine, such that the instructions, which execute via theprocessor of the computer or other programmable data processingapparatus, create means for implementing the functions/acts specified inthe flowchart and/or portion diagram portion or portions.

These computer program instructions may also be stored in a computerreadable medium that can direct a computer, other programmable dataprocessing apparatus, or other devices to function in a particularmanner, such that the instructions stored in the computer readablemedium produce an article of manufacture including instructions whichimplement the function/act specified in the flowchart and/or portiondiagram portion or portions.

The computer program instructions may also be loaded onto a computer,other programmable data processing apparatus, or other devices to causea series of operational steps to be performed on the computer, otherprogrammable apparatus or other devices to produce a computerimplemented process such that the instructions which execute on thecomputer or other programmable apparatus provide processes forimplementing the functions/acts specified in the flowchart and/orportion diagram portion or portions.

The aforementioned flowchart and diagrams illustrate the architecture,functionality, and operation of possible implementations of systems,methods and computer program products according to various embodimentsof the present invention. In this regard, each portion in the flowchartor portion diagrams may represent a module, segment, or portion of code,which comprises one or more executable instructions for implementing thespecified logical function(s). It should also be noted that, in somealternative implementations, the functions noted in the portion mayoccur out of the order noted in the figures. For example, two portionsshown in succession may, in fact, be executed substantiallyconcurrently, or the portions may sometimes be executed in the reverseorder, depending upon the functionality involved. It will also be notedthat each portion of the portion diagrams and/or flowchart illustration,and combinations of portions in the portion diagrams and/or flowchartillustration, can be implemented by special purpose hardware-basedsystems that perform the specified functions or acts, or combinations ofspecial purpose hardware and computer instructions.

In the above description, an embodiment is an example or implementationof the invention. The various appearances of “one embodiment”, “anembodiment”, “certain embodiments” or “some embodiments” do notnecessarily all refer to the same embodiments. Although various featuresof the invention may be described in the context of a single embodiment,the features may also be provided separately or in any suitablecombination. Conversely, although the invention may be described hereinin the context of separate embodiments for clarity, the invention mayalso be implemented in a single embodiment. Certain embodiments of theinvention may include features from different embodiments disclosedabove, and certain embodiments may incorporate elements from otherembodiments disclosed above. The disclosure of elements of the inventionin the context of a specific embodiment is not to be taken as limitingtheir use in the specific embodiment alone. Furthermore, it is to beunderstood that the invention can be carried out or practiced in variousways and that the invention can be implemented in certain embodimentsother than the ones outlined in the description above.

The invention is not limited to those diagrams or to the correspondingdescriptions. For example, flow need not move through each illustratedbox or state, or in exactly the same order as illustrated and described.Meanings of technical and scientific terms used herein are to becommonly understood as by one of ordinary skill in the art to which theinvention belongs, unless otherwise defined. While the invention hasbeen described with respect to a limited number of embodiments, theseshould not be construed as limitations on the scope of the invention,but rather as exemplifications of some of the preferred embodiments.Other possible variations, modifications, and applications are alsowithin the scope of the invention. Accordingly, the scope of theinvention should not be limited by what has thus far been described, butby the appended claims and their legal equivalents.

1. A method of directly measuring metrology parameters on devices, themethod comprising: measuring at least one metrology parameter from atleast one portion of a device design selected to have a plurality ofirregularly repeating units comprising specified features, along atleast one direction of the at least one portion, and calibratingsensitivity using at least one of: an intensity of diffraction ordersorthogonal to the at least one direction; introduced offsets along anon-critical direction; target cells with introduced offsets adjacent tothe device portion(s); and at least one sensitivity calibration target,wherein the measuring is carried out scatterometrically on a pluralityof targets to provide layer-specific metrology parameters, at least oneof the targets being part of the at least one device portion having N>2overlapping layers, wherein the plurality of targets comprises at leastone of: N cell pairs, each pair having opposite offsets at a differentlayer; N cells with selected intended offsets; N or fewer cells withselected intended offsets configured to utilize pupil information; andN-cell calibration targets alongside between N−1 and two overlaytargets.
 2. The method recited in claim 1, wherein the introducedoffsets are orthogonal to a critical direction of the portion of thedevice and wherein the measuring the at least one metrology parameter iscarried out without introducing an intended offset along the criticaldirection of the device portion.
 3. The method recited in claim 2,wherein a measurement direction of the adjacent target cells isperpendicular to the critical direction portion of the device portion.4. The method recited in claim 1, further comprising selectingparameters of at least one of the adjacent target cells and thesensitivity calibration targets, to reduce inaccuracy according to amodel of the inaccuracy.
 5. The method recited in claim 1, wherein theat least one sensitivity calibration target is on scribe lines.
 6. Themethod recited in claim 1, wherein the measuring the at least onemetrology parameter further comprises estimating a noise resulting fromirregularities of the device portion, being its deviations from strictperiodicity, and estimating a measurement error accordingly.
 7. Themethod recited in claim 6, wherein the at least one portion comprises aplurality of device design portions selected to yield a derived pupilplane image from respective pupil images of the portions, whichsatisfies a specified criterion with respect to the estimated noise. 8.The method recited in claim 1, wherein the targets comprise N cellpairs, each pair with opposite offsets at a different layer, at leastone of the cells being part of the device portion.
 9. The method recitedin claim 1, wherein the targets comprise N cells with selected intendedoffsets, at least one of the cells being part of the device portion andhaving a zero intended offset.
 10. The method recited in claim 1,wherein the multi-layered targets comprise N or fewer cells withselected intended offsets configured to utilize pupil information, atleast one of the cells being part of the device portion and having azero intended offset.
 11. The method recited in claim 1, wherein thetargets comprise N-cell calibration targets alongside between N−1 andtwo overlay targets at least one of the overlay targets being part ofthe device portion and having a zero intended offset.
 12. The methodrecited in claim 1 wherein the measuring is of M≧N differential signalsand comprises calculating the at least one metrology parameter therefromusing a set of corresponding M equations relating the differentialsignals to the intended offsets and the at least one metrologyparameter.
 13. The method recited in claim 12, wherein the measuring ofM signals is carried out sequentially for consecutive layers of thetargets.
 14. The method recited in claim 13, wherein the at least onemetrology parameter comprises a plurality of overlays between the Nlayers, and wherein the calculating is carried out according to:$f = \begin{pmatrix}f_{1,1} & f_{1,2} & \ldots & f_{1,N} \\f_{2,1} & f_{2,2} & \ldots & f_{2,N} \\\vdots & \vdots & \ddots & \vdots \\f_{N,1} & f_{N,2} & \ldots & f_{N,N}\end{pmatrix}$ $\begin{matrix}{F = \begin{pmatrix}F_{1,1} & F_{1,2} & \ldots & F_{1,{N - 1}} \\F_{2,1} & F_{2,2} & \ldots & F_{2,{N - 1}} \\\vdots & \vdots & \ddots & \vdots \\F_{N,1} & F_{N,2} & \ldots & F_{N,{N - 1}}\end{pmatrix}} \\{\begin{pmatrix}{f_{1,1} - f_{1,N}} & {f_{12} - f_{1N}} & \ldots & {f_{1,{N - 1}} - f_{1N}} \\{f_{2,1} - f_{2,N}} & {f_{22} - f_{2N}} & \ldots & {f_{2,{N - 1}} - f_{2N}} \\\vdots & \vdots & \ddots & \vdots \\{f_{N,1} - f_{N,N}} & {f_{N\; 2} - f_{NN}} & \ldots & {f_{N,{N - 1}} - f_{NN}}\end{pmatrix}}\end{matrix}$ $\begin{matrix}{G = \begin{pmatrix}G_{1,1} & G_{1,2} & \ldots & G_{1,{N - 1}} \\G_{2,1} & G_{2,2} & \ldots & G_{2,{N - 1}} \\\vdots & \vdots & \ddots & \vdots \\G_{{N - 1},1} & G_{{N - 1},2} & \ldots & G_{{N - 1},{N - 1}}\end{pmatrix}} \\{{= \begin{pmatrix}{F_{1,1} - F_{N,1}} & {F_{1,2} - F_{N,2}} & \ldots & {F_{1,{N - 1}} - F_{N,{N - 1}}} \\{F_{2,1} - F_{N,1}} & {F_{2,2} - F_{N,2}} & \ldots & {F_{2,{N - 1}} - F_{N,{N - 1}}} \\\vdots & \vdots & \ddots & \vdots \\{F_{{N - 1},1} - F_{N\; 1}} & {F_{{N - 1},2} - F_{N\; 2}} & \ldots & {F_{{N - 1},{N - 1}} - F_{N,{N - 1}}}\end{pmatrix}};}\end{matrix}$ ${\Delta = \begin{pmatrix}\Delta_{1} \\\Delta_{2} \\\vdots \\\Delta_{N - 1}\end{pmatrix}},{B = \begin{pmatrix}B_{1} \\B_{2} \\\vdots \\B_{N - 1}\end{pmatrix}},{\Delta_{i} = {{\sum_{k = 1}^{N - 1}{G_{ik}B_{k}}} = ({GB})_{i}}},{B = {G^{- 1}\Delta}}$${\Delta_{i} = {{D_{N} - D_{i}} = {\sum_{k = 1}^{N - 1}{B_{k} \cdot \left\lbrack {\left( {f_{i,k} - f_{i,N}} \right) - \left( {f_{N,k} - f_{N,N}} \right)} \right\rbrack}}}},;$$\begin{matrix}{D_{N} = {\sum_{k = 1}^{N - 1}{B_{k} \cdot \left( {{OVL}_{k} - F_{N,k}} \right)}}} \\{= {{\sum_{k = 1}^{N - 2}{B_{k} \cdot \left( {{OVL}_{k} - F_{N,k}} \right)}} + {B_{N - 1} \cdot \left( {{OVL}_{N - 1} - F_{N,{N - 1}}} \right)}}}\end{matrix}$${OVL}_{N - 1} = {\frac{D_{N} - {\sum_{k = 1}^{N - 2}{B_{k} \cdot \left( {{OVL}_{k} - F_{N,k}} \right)}}}{B_{N - 1}} + {F_{N,{N - 1}}.}}$15. The method recited in claim 12, wherein the measuring of M signalsis carried out simultaneously for the N layers, by carrying out themeasuring at a pupil plane with respect to the targets and usingmeasurements of a plurality of pixel positions at the pupil plane. 16.The method recited in claim 15, wherein the at least one metrologyparameter comprises a plurality of overlays between the N layers, andwherein the calculating is carried out according to:$\mspace{20mu} {\Omega = {\sum\limits_{m = 1}^{N}\; {\sum\limits_{q \in {pupil}}^{\;}\; \left\lbrack {{D_{m}(q)} - {\sum\limits_{k = 1}^{N - 1}\; {{B_{k}(q)} \cdot \left( {{OVL}_{k} - F_{mk}} \right)}}} \right\rbrack^{2}}}}$$\mspace{20mu} \begin{matrix}{\frac{\partial\Omega}{\partial{OVL}_{l}} = {\sum\limits_{m = 1}^{N}\; {\sum\limits_{q \in {pupil}}^{\;}{{B_{l}(q)}\left\lbrack {{D_{m}(q)} - {\sum\limits_{k = 1}^{N - 1}\; {{B_{k}(q)} \cdot \left( {{OVL}_{k} - F_{mk}} \right)}}} \right\rbrack}}}} \\{= 0}\end{matrix}$${\sum\limits_{k = 1}^{N - 1}\; {\left\lbrack {\sum\limits_{m = 1}^{N}\; {\sum\limits_{q \in {pupil}}^{\;}{{B_{l}(q)}{B_{k}(q)}}}} \right\rbrack \cdot {OVL}_{k}}} = {\sum\limits_{m = 1}^{N}\; {\sum\limits_{q \in {pupil}}^{\;}{{B_{l}(q)}\left\lbrack {{D_{m}(q)} + {\sum\limits_{k = 1}^{N - 1}\; {{B_{k}(q)} \cdot F_{mk}}}} \right\rbrack}}}$${\sum\limits_{k = 1}^{N - 1}{\sum\limits_{q \in {pupil}}^{\;}{{B_{l}(q)}{{B_{k}(q)} \cdot {OVL}_{k}}}}} = {\frac{1}{N}{\sum\limits_{q \in {pupil}}^{\;}{{B_{l}(q)}{\sum\limits_{m = 1}^{N}\left\lbrack {{D_{m}(q)} + {\sum\limits_{k = 1}^{N - 1}\; {{B_{k}(q)} \cdot F_{mk}}}} \right\rbrack}}}}$${{\sum\limits_{k = 1}^{N - 1}{\sum\limits_{q \in {pupil}}^{\;}{{B_{l}(q)}{{B_{k}(q)} \cdot {OVL}_{k}}}}} = {\sum\limits_{q \in {pupil}}^{\;}{{B_{l}(q)}\left\lbrack {{D_{N}(q)} + {\sum\limits_{k = 1}^{N - 1}\; {{B_{k}(q)} \cdot F_{Nk}}}} \right\rbrack}}};$$\mspace{20mu} {{W_{lk} = {\sum\limits_{q \in {pupil}}^{\;}{{B_{l}(q)}{B_{k}(q)}}}};}$$\mspace{20mu} {{V_{l} = {\sum\limits_{q \in {pupil}}^{\;}{{B_{l}(q)}\left\lbrack {{D_{N}(q)} + {\sum\limits_{k = 1}^{N - 1}\; {{B_{k}(q)} \cdot F_{Nk}}}} \right\rbrack}}};}$$\mspace{20mu} {{W_{lk} = {\sum\limits_{q \in {pupil}}^{\;}{B_{l}(q){B_{k}(q)}}}};}$$\mspace{20mu} {V_{l} = {\sum\limits_{q \in {pupil}}^{\;}{B_{l}\left( {D_{3} + {B_{1}F_{3,1}} + {B_{2}F_{3,2}}} \right)}}}$$\mspace{20mu} {{W = \begin{pmatrix}{\sum\limits_{q}^{\;}\; {B_{1}B_{1}}} & {\sum\limits_{q}^{\;}\; {B_{1}B_{2}}} \\{\sum\limits_{q}^{\;}\; {B_{2}B_{1}}} & {\sum\limits_{q}^{\;}\; {B_{2}B_{2}}}\end{pmatrix}},\mspace{20mu} {{V = \begin{pmatrix}{\sum\limits_{q}\; {B_{1}\left( {D_{3} + {B_{1}F_{3,1}} + {B_{2}F_{3,2}}} \right)}} \\{\sum\limits_{q}\; {B_{2}\left( {D_{3} + {B_{1}F_{3,1}} + {B_{2}F_{3,2}}} \right)}}\end{pmatrix}};{{OVL} = {{W^{- 1}{V\begin{pmatrix}{OVL}_{1} \\{OVL}_{2}\end{pmatrix}}} = {\begin{pmatrix}{\sum\limits_{q}^{\;}\; {B_{1}B_{1}}} & {\sum\limits_{q}^{\;}\; {B_{1}B_{2}}} \\{\sum\limits_{q}^{\;}\; {B_{2}B_{1}}} & {\sum\limits_{q}^{\;}\; {B_{2}B_{2}}}\end{pmatrix}^{- 1}{\begin{pmatrix}{\sum\limits_{q}\; {B_{1}\left( {D_{3} + {B_{1}F_{3,1}} + {B_{2}F_{3,2}}} \right)}} \\{\sum\limits_{q}\; {B_{2}\left( {D_{3} + {B_{1}F_{3,1}} + {B_{2}F_{3,2}}} \right)}}\end{pmatrix}.}}}}}}$
 17. The method recited in claim 15, wherein the atleast one metrology parameter comprises a plurality of overlays betweenthe N layers, and wherein the calculating is carried out according to:${{rOVL}\left( {k,n} \right)} \approx {{\delta_{3}(n)} - {{\overset{\sim}{f}(k)}{ɛ_{1}(n)}}}$$\begin{matrix}{{\overset{\sim}{f}(k)} = \frac{{A_{13}(k)} - {A_{12}(k)}}{{A_{13}(k)} - {A_{23}(k)}}} \\{= {\frac{1 - \frac{E_{010}{\sin \left( {\theta_{00100} - \theta_{010}} \right)}}{E_{1}^{t}{\sin \left( \theta_{00100} \right)}}}{1 - \frac{E_{010}{\sin \left( \theta_{010} \right)}}{E_{00100}{\sin \left( \theta_{00100} \right)}}}.}}\end{matrix}$
 18. The method recited in claim 1, wherein the specifiedfeatures comprise a least one set of lines and cuts.
 19. The methodrecited in claim 1, further comprising deriving at least one device-likepattern from a respective at least one device design, and designing atleast one of the targets to have regions between periodic structuresthereof at least partially filled by the at least one device-likepattern.
 20. The method recited in claim 19, further comprisingdesigning the at least one target to have sub-regions between elementsof the periodic structures at least partially filled by the at least onedevice-like pattern.
 21. The method recited in claim 1 carried out atleast partially by at least one computer processor.
 22. (canceled) 23.(canceled)
 24. A target design file of targets designed according to themethod recited in claim
 1. 25. (canceled)
 26. A metrology targetcomprising: at least one portion of a device design having N>2overlapping layers, which is selected to have a plurality of irregularlyrepeating units, having specified features, along at least one directionof the portion, and a plurality of additional cells comprising at leastmulti-layer cells and sensitivity calibration cells.
 27. The metrologytarget of claim 26, wherein the multi-layer cells comprise at least oneof: N cell pairs, each pair having opposite offsets at a differentlayer; N cells with selected intended offsets; N or fewer cells withselected intended offsets configured to utilize pupil information; andN-cell calibration targets alongside between N−1 and two overlaytargets.
 28. The metrology target of claim 26, wherein the sensitivitycalibration cells comprise at least two target cells with introducedoffsets that area adjacent to the device portion.
 29. The metrologytarget of claim 28, wherein the introduced offsets are orthogonal to acritical direction of the portion of the device and wherein the deviceportion has no intended offset along the critical direction thereof. 30.The metrology target of claim 28, wherein the parameters of at least oneof the adjacent target cells and the sensitivity calibration targets areselected to reduce inaccuracy according to a model of the inaccuracy.31. The metrology target of claim 26, wherein the sensitivitycalibration cells are on scribe lines.
 32. The metrology target of claim26, wherein the at least one portion comprises a plurality of devicedesign portions selected to yield a derived pupil plane image fromrespective pupil images of the portions, which satisfies a specifiedcriterion.
 33. The metrology target of claim 26, wherein the specifiedfeatures comprise a least one set of lines and cuts.
 34. A target designfile of the metrology target of claim
 26. 35. (canceled)
 36. A methodcomprising: configuring a multi-layered metrology target to have aplurality, M, of target cells over at least three, N≦M, target layers,each cell having at least one periodic structure in each layer, andconfiguring the periodic structures of each cell to be offset withrespect to each other by specified offsets, measuring,scatterometrically, at least M differential signals from themulti-layered metrology target, and calculating SCOL metrologyparameters from the M measurements of the multi-layered metrology targetby solving a set of M equations that relate the SCOL metrologyparameters to the differential signals and to the specified offsets. 37.The method recited in claim 36, wherein the SCOL metrology parametersare overlays between the N layers.
 38. The method recited in claim 36,wherein the calculating of the SCOL metrology parameters is carried outsequentially for consecutive layers.
 39. The method recited in claim 38,wherein the SCOL metrology parameters are overlays between the N layers,and wherein the calculating is carried out according to:$f = \begin{pmatrix}f_{1,1} & f_{1,2} & \ldots & f_{1,N} \\f_{2,1} & f_{2,2} & \ldots & f_{2,N} \\\vdots & \vdots & \ddots & \vdots \\f_{N,1} & f_{N,2} & \ldots & f_{N,N}\end{pmatrix}$ $\begin{matrix}{F = \begin{pmatrix}F_{1,1} & F_{1,2} & \ldots & F_{1,{N - 1}} \\F_{2,1} & F_{2,2} & \ldots & F_{2,{N - 1}} \\\vdots & \vdots & \ddots & \vdots \\F_{N,1} & F_{N,2} & \ldots & F_{N,{N - 1}}\end{pmatrix}} \\{\begin{pmatrix}{f_{1,1} - f_{1,N}} & {f_{12} - f_{1N}} & \ldots & {f_{1,{N - 1}} - f_{1N}} \\{f_{2,1} - f_{2,N}} & {f_{22} - f_{2N}} & \ldots & {f_{2,{N - 1}} - f_{2N}} \\\vdots & \vdots & \ddots & \vdots \\{f_{N,1} - f_{N,N}} & {f_{N\; 2} - f_{NN}} & \ldots & {f_{N,{N - 1}} - f_{NN}}\end{pmatrix}}\end{matrix}$ $\begin{matrix}{G = \begin{pmatrix}G_{1,1} & G_{1,2} & \ldots & G_{1,{N - 1}} \\G_{2,1} & G_{2,2} & \ldots & G_{2,{N - 1}} \\\vdots & \vdots & \ddots & \vdots \\G_{{N - 1},1} & G_{{N - 1},2} & \ldots & G_{{N - 1},{N - 1}}\end{pmatrix}} \\{{= \begin{pmatrix}{F_{1,1} - F_{N,1}} & {F_{1,2} - F_{N,2}} & \ldots & {F_{1,{N - 1}} - F_{N,{N - 1}}} \\{F_{2,1} - F_{N,1}} & {F_{2,2} - F_{N,2}} & \ldots & {F_{2,{N - 1}} - F_{N,{N - 1}}} \\\vdots & \vdots & \ddots & \vdots \\{F_{{N - 1},1} - F_{N\; 1}} & {F_{{N - 1},2} - F_{N\; 2}} & \ldots & {F_{{N - 1},{N - 1}} - F_{N,{N - 1}}}\end{pmatrix}};}\end{matrix}$ ${\Delta = \begin{pmatrix}\Delta_{1} \\\Delta_{2} \\\vdots \\\Delta_{N - 1}\end{pmatrix}},{B = \begin{pmatrix}B_{1} \\B_{2} \\\vdots \\B_{N - 1}\end{pmatrix}},{\Delta_{i} = {{\sum_{k = 1}^{N - 1}{G_{ik}B_{k}}} = ({GB})_{i}}},{B = {G^{- 1}\Delta}}$${\Delta_{i} = {{D_{N} - D_{i}} = {\sum_{k = 1}^{N - 1}{B_{k} \cdot \left\lbrack {\left( {f_{i,k} - f_{i,N}} \right) - \left( {f_{N,k} - f_{N,N}} \right)} \right\rbrack}}}},;$$\begin{matrix}{D_{N} = {\overset{N - 1}{\sum\limits_{k = 1}}{B_{k} \cdot \left( {{OVL}_{k} - F_{N,k}} \right)}}} \\{= {{\overset{N - 2}{\sum\limits_{k = 1}}{B_{k} \cdot \left( {{OVL}_{k} - F_{N,k}} \right)}} + {B_{N - 1} \cdot \left( {{OVL}_{N - 1} - F_{N,{N - 1}}} \right)}}}\end{matrix}$${OVL}_{N - 1} = {\frac{D_{N} - {\sum_{k = 1}^{N - 2}{B_{k} \cdot \left( {{OVL}_{k} - F_{N,k}} \right)}}}{B_{N - 1}} + {F_{N,{N - 1}}.}}$40. The method recited in claim 36, wherein the calculating of the SCOLmetrology parameters is carried out simultaneously for the layers, bycarrying out the measuring at a pupil plane with respect to the targetand using measurements of a plurality of pixel positions at the pupilplane.
 41. The method recited in claim 40, wherein the SCOL metrologyparameters are overlays between the N layers, wherein the calculating iscarried out according to:$\mspace{20mu} {\Omega = {\sum\limits_{m = 1}^{N}\; {\sum\limits_{q \in {pupil}}^{\;}\; \left\lbrack {{D_{m}(q)} - {\sum\limits_{k = 1}^{N - 1}\; {{B_{k}(q)} \cdot \left( {{OVL}_{k} - F_{mk}} \right)}}} \right\rbrack^{2}}}}$$\mspace{20mu} \begin{matrix}{\frac{\partial\Omega}{\partial{OVL}_{l}} = {\sum\limits_{m = 1}^{N}\; {\sum\limits_{q \in {pupil}}^{\;}{{B_{l}(q)}\left\lbrack {{D_{m}(q)} - {\sum\limits_{k = 1}^{N - 1}\; {{B_{k}(q)} \cdot \left( {{OVL}_{k} - F_{mk}} \right)}}} \right\rbrack}}}} \\{= 0}\end{matrix}$${\sum\limits_{k = 1}^{N - 1}\; {\left\lbrack {\sum\limits_{m = 1}^{N}\; {\sum\limits_{q \in {pupil}}^{\;}{{B_{l}(q)}{B_{k}(q)}}}} \right\rbrack \cdot {OVL}_{k}}} = {\sum\limits_{m = 1}^{N}\; {\sum\limits_{q \in {pupil}}^{\;}{{B_{l}(q)}\left\lbrack {{D_{m}(q)} + {\sum\limits_{k = 1}^{N - 1}\; {{B_{k}(q)} \cdot F_{mk}}}} \right\rbrack}}}$${\sum\limits_{k = 1}^{N - 1}{\sum\limits_{q \in {pupil}}^{\;}{{B_{l}(q)}{{B_{k}(q)} \cdot {OVL}_{k}}}}} = {\frac{1}{N}{\sum\limits_{q \in {pupil}}^{\;}{{B_{l}(q)}{\sum\limits_{m = 1}^{N}\left\lbrack {{D_{m}(q)} + {\sum\limits_{k = 1}^{N - 1}\; {{B_{k}(q)} \cdot F_{mk}}}} \right\rbrack}}}}$${{\sum\limits_{k = 1}^{N - 1}{\sum\limits_{q \in {pupil}}^{\;}{{B_{l}(q)}{{B_{k}(q)} \cdot {OVL}_{k}}}}} = {\sum\limits_{q \in {pupil}}^{\;}{{B_{l}(q)}\left\lbrack {{D_{N}(q)} + {\sum\limits_{k = 1}^{N - 1}\; {{B_{k}(q)} \cdot F_{Nk}}}} \right\rbrack}}};$$\mspace{20mu} {{W_{lk} = {\sum\limits_{q \in {pupil}}^{\;}{{B_{l}(q)}{B_{k}(q)}}}};}$$\mspace{20mu} {{V_{l} = {\sum\limits_{q \in {pupil}}^{\;}{{B_{l}(q)}\left\lbrack {{D_{N}(q)} + {\sum\limits_{k = 1}^{N - 1}\; {{B_{k}(q)} \cdot F_{Nk}}}} \right\rbrack}}};}$$\mspace{20mu} {{W_{lk} = {\sum\limits_{q \in {pupil}}^{\;}{B_{l}(q){B_{k}(q)}}}};}$$\mspace{20mu} {V_{l} = {\sum\limits_{q \in {pupil}}^{\;}{B_{l}\left( {D_{3} + {B_{1}F_{3,1}} + {B_{2}F_{3,2}}} \right)}}}$$\mspace{20mu} {{W = \begin{pmatrix}{\sum\limits_{q}^{\;}\; {B_{1}B_{1}}} & {\sum\limits_{q}^{\;}\; {B_{1}B_{2}}} \\{\sum\limits_{q}^{\;}\; {B_{2}B_{1}}} & {\sum\limits_{q}^{\;}\; {B_{2}B_{2}}}\end{pmatrix}},\mspace{20mu} {{V = \begin{pmatrix}{\sum\limits_{q}\; {B_{1}\left( {D_{3} + {B_{1}F_{3,1}} + {B_{2}F_{3,2}}} \right)}} \\{\sum\limits_{q}\; {B_{2}\left( {D_{3} + {B_{1}F_{3,1}} + {B_{2}F_{3,2}}} \right)}}\end{pmatrix}};{{OVL} = {{W^{- 1}{V\begin{pmatrix}{OVL}_{1} \\{OVL}_{2}\end{pmatrix}}} = {\begin{pmatrix}{\overset{\;}{\sum q}B_{1}B_{1}} & {\sum\limits^{\;}\; {q\; B_{1}B_{2}}} \\{\sum\limits^{\;}\; {q\; B_{2}B_{1}}} & {\sum\limits^{\;}\; {q\; B_{2}B_{2}}}\end{pmatrix}^{- 1}{\begin{pmatrix}{\sum\; {q\; {B_{1}\left( {D_{3} + {B_{1}F_{3,1}} + {B_{2}F_{3,2}}} \right)}}} \\{\sum\; {q\; {B_{2}\left( {D_{3} + {B_{1}F_{3,1}} + {B_{2}F_{3,2}}} \right)}}}\end{pmatrix}.}}}}}}$
 42. The method recited in claim 36, wherein N=3,wherein the SCOL metrology parameters are overlays between the threelayers, wherein the calculating is carried out according to:${{rOVL}\left( {k,n} \right)} \approx {{\delta_{3}(n)} - {{\overset{\sim}{f}(k)}{ɛ_{1}(n)}}}$$\begin{matrix}{{\overset{\sim}{f}(k)} = \frac{{A_{13}(k)} - {A_{12}(k)}}{{A_{13}(k)} - {A_{23}(k)}}} \\{= {\frac{1 - \frac{E_{010}{\sin \left( {\theta_{00100} - \theta_{010}} \right)}}{E_{1}^{t}{\sin \left( \theta_{00100} \right)}}}{1 - \frac{E_{010}{\sin \left( \theta_{010} \right)}}{E_{00100}{\sin \left( \theta_{00100} \right)}}}.}}\end{matrix}$
 43. The method recited in claim 36, carried out at leastpartially by at least one computer processor.
 44. (canceled) 45.(canceled)
 46. A target design file of targets designed according to themethod recited in claim
 36. 47. (canceled)
 48. A multi-layered metrologytarget comprising a plurality of target cells over at least three targetlayers, each cell having at least one periodic structure in each layer,wherein the periodic structures of each cell are offset with respect toeach other by specified offsets.
 49. (canceled)
 50. A method comprising:deriving a plurality of device-like patterns from a respective pluralityof device designs, wherein device-like patterns comprise specifiedfeatures, and designing a metrology target using the derived device-likepatterns as irregularly repeating units along at least one direction ofthe target.
 51. The method recited in claim 50, further comprisingvarying along the at least one direction of the target at least one of:a unit length, characteristics of lines in the unit and characteristicsof cuts in the unit.
 52. The method recited in claim 50, furthercomprising estimating a noise resulting from irregularities of themetrology target, being its deviations from strict periodicity.
 53. Themethod recited in claim 52, further comprising estimating a measurementerror according to the estimated noise.
 54. The method recited in claim52, further comprising designing or selecting appropriate patternsaccording to specified noise thresholds.
 55. The method recited in claim50, wherein the specified features comprise a least one set of lines andcuts.
 56. The method recited in claim 50, wherein the at least onedirection comprises two perpendicular directions of the target.
 57. Themethod recited in claim 50, wherein the target comprises at least twolayers.
 58. The method recited in claim 50, further comprising producingthe designed metrology target.
 59. The method recited in claim 58,further comprising deriving a metrology signal from the producedmetrology target.
 60. The method recited in claim 50, carried out atleast partially by at least one computer processor.
 61. (canceled) 62.(canceled)
 63. A target design file of targets designed according to themethod recited in claim
 50. 64. (canceled)
 65. A metrology targetcomprising irregularly repeating units along at least one direction ofthe target, wherein the units comprise device-like patterns havingspecified features, which are derived from respective device designs.66. The metrology target of claim 65, wherein at least one of: a unitlength, characteristics of lines in the unit and characteristics of cutsin the unit; is varied along the at least one direction of the target.67. The metrology target of claim 65, wherein the at least one directioncomprises two perpendicular directions of the target.
 68. The metrologytarget of claim 65, wherein the target comprises at least two layers.69. The metrology target of claim 65, wherein the specified featurescomprise a least one set of lines and cuts.
 70. (canceled)
 71. A methodcomprising: deriving at least one device-like pattern from a respectiveat least one device design, and designing a metrology target, comprisinga plurality of periodic structures, to have regions between the periodicstructures at least partially filled by the at least one device-likepattern.
 72. The method recited in claim 71, further comprisingdesigning the metrology target to have sub-regions between elements ofthe periodic structures at least partially filled by the at least onedevice-like pattern.
 73. The method recited in claim 71, wherein thetarget comprises at least two layers.
 74. The method recited in claim71, further comprising producing the designed metrology target.
 75. Themethod recited in claim 74, further comprising deriving a metrologysignal from the produced metrology target.
 76. The method recited inclaim 71 carried out at least partially by at least one computerprocessor.
 77. (canceled)
 78. (canceled)
 79. A target design file oftargets designed according to the method recited in claim
 71. 80.(canceled)
 81. A metrology target comprising a plurality of periodicstructures and regions between the periodic structures which are atleast partially filled by at least one device-like pattern derived froma respective at least one device design.
 82. The metrology target ofclaim 81, wherein sub-regions between elements of the periodicstructures are at least partially filled by the at least one device-likepattern.
 83. The metrology target of claim 81, wherein the targetcomprises at least two layers.
 84. (canceled)
 85. A method comprisingmeasuring at least one metrology parameter in at least one target cellwithout introducing an intended offset along a critical measurementdirection into the at least one target cell by calibrating at least onesensitivity parameter using offsets in at least one of: (i) anorthogonal, non-critical measurement direction and (ii) at least oneadditional target cell other than the at least one target cell.
 86. Themethod recited in claim 85, wherein the offsets in the orthogonaldirection are introduced into at least one additional target cell otherthan the at least one target cell.
 87. The method recited in claim 86,wherein the at least one additional target cell is adjacent to the atleast one target cell.
 88. The method recited in claim 86, wherein theat least one additional target cell is a calibration target positionedon scribe lines.
 89. The method recited in claim 86, further comprisingselecting parameters of the at least one additional target cell toreduce inaccuracy according to a model of the inaccuracy.
 90. The methodrecited in claim 85, wherein the at least one target cell comprises atleast a part of a device design.
 91. The method recited in claim 90,further comprising introducing the offsets in the orthogonal directioninto at least one additional target cell adjacent to the at least onetarget cell.
 92. The method recited in claim 90, wherein the offsets areintroduced along the orthogonal, non-critical measurement direction ofthe device design.
 93. The method recited in claim 90, furthercomprising introducing the offsets in at least one calibration targetpositioned on scribe lines.
 94. (canceled)
 95. (canceled)
 96. A targetdesign file of targets comprising cells designed according to the methodrecited in claim
 85. 97. (canceled)
 98. A metrology target comprising:at least one target cell without an intended offset along a criticalmeasurement direction of the at least one target cell, and at least twoadditional cells having intended offsets along the critical measurementdirection of the at least one target cell.
 99. The metrology target ofclaim 98, wherein the at least two additional cells have an orthogonalcritical measurement direction with respect to the at least one targetcell.
 100. The metrology target of claim 98, wherein the at least twoadditional cells are adjacent to the at least one target cell.
 101. Themetrology target of claim 98, wherein the at least two additional cellsare calibration targets on scribe lines.
 102. The metrology target ofclaim 98, wherein the at least one target cell comprises at least a partof a device design.
 103. (canceled)
 104. A metrology target comprisingat least one target cell without an intended offset along a criticalmeasurement direction of the at least one target cell, and havingintended offsets along a non-critical measurement direction of the atleast one target cell.
 105. (canceled)